कोण \(150^\circ\) को रेडियन में बदलने पर कौन सा मान मिलता है?
Which value is obtained when the angle \(150^\circ\) is converted into radians?
#trigonometric-functions
#angles
#radian-degree
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A \(\frac{2\pi}{3}\)
B \(\frac{3\pi}{4}\)
C \(\frac{5\pi}{6}\)
D \(\frac{7\pi}{6}\)
Explanation opens after your attempt
Correct Answer
C. \(\frac{5\pi}{6}\)
Step 1
Concept
Multiply degrees by \( \frac{\pi}{180} \) to convert into radians. In exams identify multiples of \(30^\circ\) quickly.
Step 2
Why this answer is correct
The correct answer is C. \(\frac{5\pi}{6}\). Multiply degrees by \( \frac{\pi}{180} \) to convert into radians. In exams identify multiples of \(30^\circ\) quickly.
Step 3
Exam Tip
डिग्री को रेडियन में बदलने के लिए \( \frac{\pi}{180} \) से गुणा करते हैं। परीक्षा में \(30^\circ\) के गुणकों को जल्दी पहचानें।
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कोण \(-\frac{7\pi}{6}\) का \(0^\circ\) से \(360^\circ\) के बीच सहप्रारंभी कोण क्या होगा?
What is the coterminal angle of \(-\frac{7\pi}{6}\) between \(0^\circ\) and \(360^\circ\)?
#trigonometric-functions
#coterminal-angle
#principal-angle
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A \(120^\circ\)
B \(150^\circ\)
C \(210^\circ\)
D \(330^\circ\)
Explanation opens after your attempt
Correct Answer
B. \(150^\circ\)
Step 1
Concept
\(-\frac{7\pi}{6}=-210^\circ\) and adding \(360^\circ\) gives \(150^\circ\). For a negative angle add \(360^\circ\) to get the principal angle.
Step 2
Why this answer is correct
The correct answer is B. \(150^\circ\). \(-\frac{7\pi}{6}=-210^\circ\) and adding \(360^\circ\) gives \(150^\circ\). For a negative angle add \(360^\circ\) to get the principal angle.
Step 3
Exam Tip
\(-\frac{7\pi}{6}=-210^\circ\) और \(360^\circ\) जोड़ने पर \(150^\circ\) मिलता है। नकारात्मक कोण में \(360^\circ\) जोड़कर मुख्य कोण खोजें।
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कोण \(920^\circ\) का सबसे छोटा धनात्मक सहप्रारंभी कोण क्या है?
What is the least positive coterminal angle of \(920^\circ\)?
#trigonometric-functions
#coterminal-angle
#degree-measure
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A \(160^\circ\)
B \(180^\circ\)
C \(200^\circ\)
D \(220^\circ\)
Explanation opens after your attempt
Correct Answer
C. \(200^\circ\)
Step 1
Concept
Since \(920^\circ-720^\circ=200^\circ\). Subtract multiples of \(360^\circ\) from large angles.
Step 2
Why this answer is correct
The correct answer is C. \(200^\circ\). Since \(920^\circ-720^\circ=200^\circ\). Subtract multiples of \(360^\circ\) from large angles.
Step 3
Exam Tip
\(920^\circ-720^\circ=200^\circ\) होता है। बड़े कोण में \(360^\circ\) के गुणज घटाएं।
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यदि कोई कोण (3150') है तो उसका रेडियन माप क्या होगा?
If an angle is (3150') then what is its radian measure?
#trigonometric-functions
#minutes-to-radians
#angle-conversion
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A \(\frac{5\pi}{24}\)
B \(\frac{7\pi}{24}\)
C \(\frac{11\pi}{24}\)
D \(\frac{13\pi}{24}\)
Explanation opens after your attempt
Correct Answer
B. \(\frac{7\pi}{24}\)
Step 1
Concept
\(3150'=52.5^\circ\) and \(52.5^\circ=\frac{7\pi}{24}\). Convert minutes into degrees first.
Step 2
Why this answer is correct
The correct answer is B. \(\frac{7\pi}{24}\). \(3150'=52.5^\circ\) and \(52.5^\circ=\frac{7\pi}{24}\). Convert minutes into degrees first.
Step 3
Exam Tip
\(3150'=52.5^\circ\) और \(52.5^\circ=\frac{7\pi}{24}\) है। पहले मिनट को डिग्री में बदलें।
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किसी कोण का पूरक कोण उससे \(24^\circ\) अधिक है। वह कोण क्या है?
The complement of an angle is \(24^\circ\) more than the angle. What is the angle?
#trigonometric-functions
#complementary-angles
#angle-equation
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A \(30^\circ\)
B \(33^\circ\)
C \(36^\circ\)
D \(42^\circ\)
Explanation opens after your attempt
Correct Answer
B. \(33^\circ\)
Step 1
Concept
If the angle is (x) then \(90^\circ-x=x+24^\circ\). Remember complementary angles add to \(90^\circ\).
Step 2
Why this answer is correct
The correct answer is B. \(33^\circ\). If the angle is (x) then \(90^\circ-x=x+24^\circ\). Remember complementary angles add to \(90^\circ\).
Step 3
Exam Tip
यदि कोण (x) है तो \(90^\circ-x=x+24^\circ\)। पूरक कोणों का योग \(90^\circ\) याद रखें।
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किसी कोण का संपूरक कोण उस कोण का (3) गुना है। वह कोण क्या होगा?
The supplement of an angle is (3) times the angle. What is the angle?
#trigonometric-functions
#supplementary-angles
#angle-equation
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A \(36^\circ\)
B \(40^\circ\)
C \(45^\circ\)
D \(60^\circ\)
Explanation opens after your attempt
Correct Answer
C. \(45^\circ\)
Step 1
Concept
If the angle is (x) then \(180^\circ-x=3x\) gives \(x=45^\circ\). Supplementary angles add to \(180^\circ\).
Step 2
Why this answer is correct
The correct answer is C. \(45^\circ\). If the angle is (x) then \(180^\circ-x=3x\) gives \(x=45^\circ\). Supplementary angles add to \(180^\circ\).
Step 3
Exam Tip
यदि कोण (x) है तो \(180^\circ-x=3x\) से \(x=45^\circ\) मिलता है। संपूरक कोणों का योग \(180^\circ\) होता है।
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(2.75) पूर्ण चक्करों के बराबर कोण का रेडियन माप क्या है?
What is the radian measure of an angle equal to (2.75) complete revolutions?
#trigonometric-functions
#revolution-to-radian
#angle-measure
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A \(\frac{9\pi}{2}\)
B \(\frac{11\pi}{2}\)
C \(\frac{13\pi}{2}\)
D \(\frac{15\pi}{2}\)
Explanation opens after your attempt
Correct Answer
B. \(\frac{11\pi}{2}\)
Step 1
Concept
One revolution is \(2\pi\) radians. Write \(2.75\times2\pi=\frac{11\pi}{2}\).
Step 2
Why this answer is correct
The correct answer is B. \(\frac{11\pi}{2}\). One revolution is \(2\pi\) radians. Write \(2.75\times2\pi=\frac{11\pi}{2}\).
Step 3
Exam Tip
एक चक्कर \(2\pi\) रेडियन होता है। \(2.75\times2\pi=\frac{11\pi}{2}\) लिखें।
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त्रिज्या (14) सेमी वाले वृत्त में केंद्रीय कोण \(\frac{3\pi}{7}\) हो तो चाप की लंबाई क्या होगी?
In a circle of radius (14) cm the central angle is \(\frac{3\pi}{7}\). What is the arc length?
#trigonometric-functions
#arc-length
#radian-measure
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A \(4\pi\) सेमी / \(4\pi\) cm
B \(5\pi\) सेमी / \(5\pi\) cm
C \(6\pi\) सेमी / \(6\pi\) cm
D \(7\pi\) सेमी / \(7\pi\) cm
Explanation opens after your attempt
Correct Answer
C. \(6\pi\) सेमी / \(6\pi\) cm
Step 1
Concept
Arc length is \(s=r\theta\). So \(s=14\times\frac{3\pi}{7}=6\pi\) cm.
Step 2
Why this answer is correct
The correct answer is C. \(6\pi\) सेमी / \(6\pi\) cm. Arc length is \(s=r\theta\). So \(s=14\times\frac{3\pi}{7}=6\pi\) cm.
Step 3
Exam Tip
चाप लंबाई \(s=r\theta\) होती है। इसलिए \(s=14\times\frac{3\pi}{7}=6\pi\) सेमी।
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त्रिज्या (10) सेमी और कोण \(\frac{2\pi}{5}\) वाले त्रिज्यखंड का परिमाप क्या है?
What is the perimeter of a sector with radius (10) cm and angle \(\frac{2\pi}{5}\)?
#trigonometric-functions
#sector-perimeter
#arc-length
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A \(20+4\pi\) सेमी / \(20+4\pi\) cm
B \(10+4\pi\) सेमी / \(10+4\pi\) cm
C \(20+2\pi\) सेमी / \(20+2\pi\) cm
D \(10+2\pi\) सेमी / \(10+2\pi\) cm
Explanation opens after your attempt
Correct Answer
A. \(20+4\pi\) सेमी / \(20+4\pi\) cm
Step 1
Concept
Perimeter is \(2r+r\theta\). So \(20+10\times\frac{2\pi}{5}=20+4\pi\) cm.
Step 2
Why this answer is correct
The correct answer is A. \(20+4\pi\) सेमी / \(20+4\pi\) cm. Perimeter is \(2r+r\theta\). So \(20+10\times\frac{2\pi}{5}=20+4\pi\) cm.
Step 3
Exam Tip
परिमाप \(2r+r\theta\) होता है। इसलिए \(20+10\times\frac{2\pi}{5}=20+4\pi\) सेमी।
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यदि कोणीय चाल (9) चक्कर प्रति मिनट है तो रेडियन प्रति सेकंड में मान क्या होगा?
If angular speed is (9) revolutions per minute then what is its value in radians per second?
#trigonometric-functions
#angular-speed
#radian-per-second
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A \(\frac{\pi}{10}\)
B \(\frac{3\pi}{10}\)
C \(\frac{3\pi}{5}\)
D \(\frac{9\pi}{10}\)
Explanation opens after your attempt
Correct Answer
B. \(\frac{3\pi}{10}\)
Step 1
Concept
(9) revolutions per minute equals \(18\pi\) radians per minute. Dividing by (60) gives \(\frac{3\pi}{10}\).
Step 2
Why this answer is correct
The correct answer is B. \(\frac{3\pi}{10}\). (9) revolutions per minute equals \(18\pi\) radians per minute. Dividing by (60) gives \(\frac{3\pi}{10}\).
Step 3
Exam Tip
(9) चक्कर प्रति मिनट \(=18\pi\) रेडियन प्रति मिनट है। (60) से भाग देने पर \(\frac{3\pi}{10}\) मिलता है।
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घड़ी की मिनट सुई (25) मिनट में कितने रेडियन घूमती है?
Through how many radians does the minute hand of a clock turn in (25) minutes?
#trigonometric-functions
#clock-angle
#radian-measure
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A \(\frac{\pi}{2}\)
B \(\frac{2\pi}{3}\)
C \(\frac{5\pi}{6}\)
D \(\pi\)
Explanation opens after your attempt
Correct Answer
C. \(\frac{5\pi}{6}\)
Step 1
Concept
The minute hand turns \(2\pi\) in (60) minutes. In (25) minutes the angle is \(\frac{25}{60}\times2\pi=\frac{5\pi}{6}\).
Step 2
Why this answer is correct
The correct answer is C. \(\frac{5\pi}{6}\). The minute hand turns \(2\pi\) in (60) minutes. In (25) minutes the angle is \(\frac{25}{60}\times2\pi=\frac{5\pi}{6}\).
Step 3
Exam Tip
मिनट सुई (60) मिनट में \(2\pi\) घूमती है। (25) मिनट में कोण \(\frac{25}{60}\times2\pi=\frac{5\pi}{6}\) है।
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घड़ी में (2:40) पर घंटे और मिनट की सुइयों के बीच छोटा कोण क्या है?
What is the smaller angle between the hour and minute hands at (2:40)?
#trigonometric-functions
#clock-angle
#degree-measure
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A \(140^\circ\)
B \(150^\circ\)
C \(160^\circ\)
D \(170^\circ\)
Explanation opens after your attempt
Correct Answer
C. \(160^\circ\)
Step 1
Concept
The minute hand is at \(240^\circ\) and the hour hand is at \(80^\circ\). The difference is \(160^\circ\).
Step 2
Why this answer is correct
The correct answer is C. \(160^\circ\). The minute hand is at \(240^\circ\) and the hour hand is at \(80^\circ\). The difference is \(160^\circ\).
Step 3
Exam Tip
मिनट सुई \(240^\circ\) पर और घंटे की सुई \(80^\circ\) पर होती है। अंतर \(160^\circ\) है।
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कोण \(-850^\circ\) की अंतिम भुजा किस चतुर्थांश में होगी?
In which quadrant will the terminal side of \(-850^\circ\) lie?
#trigonometric-functions
#quadrant
#coterminal-angle
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A प्रथम / First
B द्वितीय / Second
C तृतीय / Third
D चतुर्थ / Fourth
Explanation opens after your attempt
Correct Answer
C. तृतीय / Third
Step 1
Concept
\(-850^\circ+1080^\circ=230^\circ\). \(230^\circ\) lies in the third quadrant.
Step 2
Why this answer is correct
The correct answer is C. तृतीय / Third. \(-850^\circ+1080^\circ=230^\circ\). \(230^\circ\) lies in the third quadrant.
Step 3
Exam Tip
\(-850^\circ+1080^\circ=230^\circ\) है। \(230^\circ\) तृतीय चतुर्थांश में आता है।
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कोण \(1280^\circ\) का संदर्भ कोण क्या है?
What is the reference angle of \(1280^\circ\)?
#trigonometric-functions
#reference-angle
#degree-measure
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A \(20^\circ\)
B \(40^\circ\)
C \(60^\circ\)
D \(80^\circ\)
Explanation opens after your attempt
Correct Answer
A. \(20^\circ\)
Step 1
Concept
\(1280^\circ-1080^\circ=200^\circ\). In the third quadrant the reference angle is \(200^\circ-180^\circ=20^\circ\).
Step 2
Why this answer is correct
The correct answer is A. \(20^\circ\). \(1280^\circ-1080^\circ=200^\circ\). In the third quadrant the reference angle is \(200^\circ-180^\circ=20^\circ\).
Step 3
Exam Tip
\(1280^\circ-1080^\circ=200^\circ\) है। तृतीय चतुर्थांश में संदर्भ कोण \(200^\circ-180^\circ=20^\circ\) होता है।
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कोण \(-\frac{3\pi}{4}\) के सभी सहप्रारंभी कोण किस रूप में लिखे जाएंगे?
How will all coterminal angles of \(-\frac{3\pi}{4}\) be written?
#trigonometric-functions
#general-coterminal-angle
#radian-measure
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A \(-\frac{3\pi}{4}+n\pi\)
B \(-\frac{3\pi}{4}+2n\pi\)
C \(\frac{3\pi}{4}+2n\pi\)
D \(-\frac{3\pi}{4}-n\pi\)
Explanation opens after your attempt
Correct Answer
B. \(-\frac{3\pi}{4}+2n\pi\)
Step 1
Concept
Coterminal angles are formed by adding integral multiples of \(2\pi\). Hence the form is \(-\frac{3\pi}{4}+2n\pi\).
Step 2
Why this answer is correct
The correct answer is B. \(-\frac{3\pi}{4}+2n\pi\). Coterminal angles are formed by adding integral multiples of \(2\pi\). Hence the form is \(-\frac{3\pi}{4}+2n\pi\).
Step 3
Exam Tip
सहप्रारंभी कोणों में \(2\pi\) के पूर्ण गुणज जोड़े जाते हैं। इसलिए रूप \(-\frac{3\pi}{4}+2n\pi\) है।
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यदि कोण की अंतिम भुजा ऋणात्मक (y)-अक्ष पर है तो सबसे छोटा धनात्मक रेडियन कोण क्या होगा?
If the terminal side of an angle lies on the negative (y)-axis then what is the least positive radian angle?
#trigonometric-functions
#axis-angle
#radian-measure
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A \(\frac{\pi}{2}\)
B \(\pi\)
C \(\frac{3\pi}{2}\)
D \(2\pi\)
Explanation opens after your attempt
Correct Answer
C. \(\frac{3\pi}{2}\)
Step 1
Concept
The negative (y)-axis is at \(270^\circ\). Its radian measure is \(\frac{3\pi}{2}\).
Step 2
Why this answer is correct
The correct answer is C. \(\frac{3\pi}{2}\). The negative (y)-axis is at \(270^\circ\). Its radian measure is \(\frac{3\pi}{2}\).
Step 3
Exam Tip
ऋणात्मक (y)-अक्ष \(270^\circ\) पर होता है। इसका रेडियन माप \(\frac{3\pi}{2}\) है।
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कोण \(23^\circ45'\) को रेडियन में बदलें।
Convert the angle \(23^\circ45'\) into radians.
#trigonometric-functions
#dms-to-radians
#angle-conversion
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A \(\frac{17\pi}{144}\)
B \(\frac{19\pi}{144}\)
C \(\frac{23\pi}{144}\)
D \(\frac{25\pi}{144}\)
Explanation opens after your attempt
Correct Answer
B. \(\frac{19\pi}{144}\)
Step 1
Concept
\(23^\circ45'=\frac{95}{4}^\circ\). In radians it is \(\frac{95}{4}\times\frac{\pi}{180}=\frac{19\pi}{144}\).
Step 2
Why this answer is correct
The correct answer is B. \(\frac{19\pi}{144}\). \(23^\circ45'=\frac{95}{4}^\circ\). In radians it is \(\frac{95}{4}\times\frac{\pi}{180}=\frac{19\pi}{144}\).
Step 3
Exam Tip
\(23^\circ45'=\frac{95}{4}^\circ\) होता है। रेडियन में \(\frac{95}{4}\times\frac{\pi}{180}=\frac{19\pi}{144}\) है।
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रेडियन कोण \(\frac{17\pi}{12}\) का डिग्री माप क्या होगा?
What is the degree measure of the radian angle \(\frac{17\pi}{12}\)?
#trigonometric-functions
#radian-to-degree
#angle-conversion
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A \(245^\circ\)
B \(255^\circ\)
C \(265^\circ\)
D \(275^\circ\)
Explanation opens after your attempt
Correct Answer
B. \(255^\circ\)
Step 1
Concept
Multiply radians by \(\frac{180}{\pi}\) to convert into degrees. \(\frac{17\pi}{12}\times\frac{180}{\pi}=255^\circ\).
Step 2
Why this answer is correct
The correct answer is B. \(255^\circ\). Multiply radians by \(\frac{180}{\pi}\) to convert into degrees. \(\frac{17\pi}{12}\times\frac{180}{\pi}=255^\circ\).
Step 3
Exam Tip
रेडियन को डिग्री में बदलने के लिए \(\frac{180}{\pi}\) से गुणा करें। \(\frac{17\pi}{12}\times\frac{180}{\pi}=255^\circ\) है।
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कोण \(\frac{5\pi}{3}\) के लिए चतुर्थांश और संदर्भ कोण कौन सा है?
For the angle \(\frac{5\pi}{3}\) which quadrant and reference angle are correct?
#trigonometric-functions
#reference-angle
#quadrant
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A चतुर्थ चतुर्थांश और \(\frac{\pi}{3}\) / Fourth quadrant and \(\frac{\pi}{3}\)
B तृतीय चतुर्थांश और \(\frac{\pi}{3}\) / Third quadrant and \(\frac{\pi}{3}\)
C चतुर्थ चतुर्थांश और \(\frac{\pi}{6}\) / Fourth quadrant and \(\frac{\pi}{6}\)
D द्वितीय चतुर्थांश और \(\frac{\pi}{3}\) / Second quadrant and \(\frac{\pi}{3}\)
Explanation opens after your attempt
Correct Answer
A. चतुर्थ चतुर्थांश और \(\frac{\pi}{3}\) / Fourth quadrant and \(\frac{\pi}{3}\)
Step 1
Concept
\(\frac{5\pi}{3}=300^\circ\) which lies in the fourth quadrant. The reference angle is \(360^\circ-300^\circ=60^\circ=\frac{\pi}{3}\).
Step 2
Why this answer is correct
The correct answer is A. चतुर्थ चतुर्थांश और \(\frac{\pi}{3}\) / Fourth quadrant and \(\frac{\pi}{3}\). \(\frac{5\pi}{3}=300^\circ\) which lies in the fourth quadrant. The reference angle is \(360^\circ-300^\circ=60^\circ=\frac{\pi}{3}\).
Step 3
Exam Tip
\(\frac{5\pi}{3}=300^\circ\) होता है जो चतुर्थ चतुर्थांश में है। संदर्भ कोण \(360^\circ-300^\circ=60^\circ=\frac{\pi}{3}\) है।
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\(\frac{19\pi}{4}\) का (0) और \(2\pi\) के बीच सहप्रारंभी कोण क्या है?
What is the coterminal angle of \(\frac{19\pi}{4}\) between (0) and \(2\pi\)?
#trigonometric-functions
#coterminal-angle
#radian-measure
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A \(\frac{\pi}{4}\)
B \(\frac{\pi}{2}\)
C \(\frac{3\pi}{4}\)
D \(\frac{5\pi}{4}\)
Explanation opens after your attempt
Correct Answer
C. \(\frac{3\pi}{4}\)
Step 1
Concept
\(\frac{19\pi}{4}-4\pi=\frac{3\pi}{4}\). Subtract multiples of \(2\pi\) to get the principal angle.
Step 2
Why this answer is correct
The correct answer is C. \(\frac{3\pi}{4}\). \(\frac{19\pi}{4}-4\pi=\frac{3\pi}{4}\). Subtract multiples of \(2\pi\) to get the principal angle.
Step 3
Exam Tip
\(\frac{19\pi}{4}-4\pi=\frac{3\pi}{4}\) है। \(2\pi\) के गुणज घटाकर मुख्य कोण पाएं।
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यदि \(\frac{7\pi}{18}\) और (x) संपूरक कोण हैं तो (x) क्या होगा?
If \(\frac{7\pi}{18}\) and (x) are supplementary angles then what is (x)?
#trigonometric-functions
#supplementary-angles
#radian-measure
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A \(\frac{5\pi}{18}\)
B \(\frac{7\pi}{18}\)
C \(\frac{11\pi}{18}\)
D \(\frac{13\pi}{18}\)
Explanation opens after your attempt
Correct Answer
C. \(\frac{11\pi}{18}\)
Step 1
Concept
Supplementary angles add to \(\pi\). Hence \(x=\pi-\frac{7\pi}{18}=\frac{11\pi}{18}\).
Step 2
Why this answer is correct
The correct answer is C. \(\frac{11\pi}{18}\). Supplementary angles add to \(\pi\). Hence \(x=\pi-\frac{7\pi}{18}=\frac{11\pi}{18}\).
Step 3
Exam Tip
संपूरक कोणों का योग \(\pi\) होता है। इसलिए \(x=\pi-\frac{7\pi}{18}=\frac{11\pi}{18}\) है।
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यदि कोई कोण \(\frac{2}{5}\) रेडियन है तो उसका पूरक कोण क्या होगा?
If an angle is \(\frac{2}{5}\) radians then what is its complement?
#trigonometric-functions
#complementary-angles
#radian-measure
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A \(\frac{\pi}{2}-\frac{2}{5}\)
B \(\pi-\frac{2}{5}\)
C \(\frac{\pi}{2}+\frac{2}{5}\)
D \(2\pi-\frac{2}{5}\)
Explanation opens after your attempt
Correct Answer
A. \(\frac{\pi}{2}-\frac{2}{5}\)
Step 1
Concept
In radians complementary angles add to \(\frac{\pi}{2}\). So the answer is \(\frac{\pi}{2}-\frac{2}{5}\).
Step 2
Why this answer is correct
The correct answer is A. \(\frac{\pi}{2}-\frac{2}{5}\). In radians complementary angles add to \(\frac{\pi}{2}\). So the answer is \(\frac{\pi}{2}-\frac{2}{5}\).
Step 3
Exam Tip
रेडियन में पूरक कोणों का योग \(\frac{\pi}{2}\) होता है। इसलिए उत्तर \(\frac{\pi}{2}-\frac{2}{5}\) है।
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यदि चाप की लंबाई (22) सेमी और त्रिज्या (7) सेमी है तो केंद्रीय कोण रेडियन में क्या होगा?
If the arc length is (22) cm and the radius is (7) cm then what is the central angle in radians?
#trigonometric-functions
#arc-length
#central-angle
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A \(\frac{7}{22}\)
B \(\frac{22}{7}\)
C \(\frac{11}{7}\)
D \(\frac{44}{7}\)
Explanation opens after your attempt
Correct Answer
B. \(\frac{22}{7}\)
Step 1
Concept
\(\theta=\frac{s}{r}\). Hence \(\theta=\frac{22}{7}\) radians.
Step 2
Why this answer is correct
The correct answer is B. \(\frac{22}{7}\). \(\theta=\frac{s}{r}\). Hence \(\theta=\frac{22}{7}\) radians.
Step 3
Exam Tip
\(\theta=\frac{s}{r}\) होता है। इसलिए \(\theta=\frac{22}{7}\) रेडियन है।
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त्रिज्या (6) सेमी और केंद्रीय कोण \(\frac{5\pi}{9}\) वाले त्रिज्यखंड का क्षेत्रफल क्या है?
What is the area of a sector with radius (6) cm and central angle \(\frac{5\pi}{9}\)?
#trigonometric-functions
#sector-area
#radian-measure
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A \(8\pi\) वर्ग सेमी / \(8\pi\) sq cm
B \(9\pi\) वर्ग सेमी / \(9\pi\) sq cm
C \(10\pi\) वर्ग सेमी / \(10\pi\) sq cm
D \(12\pi\) वर्ग सेमी / \(12\pi\) sq cm
Explanation opens after your attempt
Correct Answer
C. \(10\pi\) वर्ग सेमी / \(10\pi\) sq cm
Step 1
Concept
Sector area is \(\frac{1}{2}r^2\theta\). So \(\frac{1}{2}\times36\times\frac{5\pi}{9}=10\pi\).
Step 2
Why this answer is correct
The correct answer is C. \(10\pi\) वर्ग सेमी / \(10\pi\) sq cm. Sector area is \(\frac{1}{2}r^2\theta\). So \(\frac{1}{2}\times36\times\frac{5\pi}{9}=10\pi\).
Step 3
Exam Tip
त्रिज्यखंड क्षेत्रफल \(\frac{1}{2}r^2\theta\) होता है। इसलिए \(\frac{1}{2}\times36\times\frac{5\pi}{9}=10\pi\) है।
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लगभग (1) रेडियन कितने डिग्री के बराबर होता है?
Approximately (1) radian is equal to how many degrees?
#trigonometric-functions
#one-radian
#degree-measure
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A \(45.0^\circ\)
B \(52.5^\circ\)
C \(57.3^\circ\)
D \(60.0^\circ\)
Explanation opens after your attempt
Correct Answer
C. \(57.3^\circ\)
Step 1
Concept
(1) radian \(=\frac{180^\circ}{\pi}\approx57.3^\circ\). In approximation questions use \(\pi\approx3.14\).
Step 2
Why this answer is correct
The correct answer is C. \(57.3^\circ\). (1) radian \(=\frac{180^\circ}{\pi}\approx57.3^\circ\). In approximation questions use \(\pi\approx3.14\).
Step 3
Exam Tip
(1) रेडियन \(=\frac{180^\circ}{\pi}\approx57.3^\circ\) होता है। अनुमान वाले प्रश्नों में \(\pi\approx3.14\) लें।
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यदि चाप की लंबाई वृत्त के व्यास के बराबर है तो केंद्रीय कोण रेडियन में क्या होगा?
If the arc length is equal to the diameter of the circle then what is the central angle in radians?
#trigonometric-functions
#arc-length
#central-angle
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A \(\frac{1}{2}\)
B (1)
C (2)
D \(\pi\)
Explanation opens after your attempt
Step 1
Concept
Diameter is (2r) and \(\theta=\frac{s}{r}\). Hence \(\theta=\frac{2r}{r}=2\) radians.
Step 2
Why this answer is correct
The correct answer is C. (2). Diameter is (2r) and \(\theta=\frac{s}{r}\). Hence \(\theta=\frac{2r}{r}=2\) radians.
Step 3
Exam Tip
व्यास (2r) होता है और \(\theta=\frac{s}{r}\) है। इसलिए \(\theta=\frac{2r}{r}=2\) रेडियन।
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यदि \(\pi=\frac{22}{7}\) लेकर त्रिज्या (35) सेमी का पहिया (220) सेमी चलता है तो वह कितने चक्कर लगाएगा?
Using \(\pi=\frac{22}{7}\) how many revolutions will a wheel of radius (35) cm make while moving (220) cm?
#trigonometric-functions
#revolution
#circumference
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A \(\frac{1}{2}\)
B (1)
C \(\frac{3}{2}\)
D (2)
Explanation opens after your attempt
Step 1
Concept
Distance in one revolution is \(2\pi r=220\) cm. Hence the number of revolutions is (1).
Step 2
Why this answer is correct
The correct answer is B. (1). Distance in one revolution is \(2\pi r=220\) cm. Hence the number of revolutions is (1).
Step 3
Exam Tip
एक चक्कर की दूरी \(2\pi r=220\) सेमी है। इसलिए कुल चक्कर (1) होगा।
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कोण \(54^\circ\) को रेडियन में बदलें।
Convert the angle \(54^\circ\) into radians.
#trigonometric-functions
#degree-to-radian
#angle-conversion
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A \(\frac{3\pi}{10}\)
B \(\frac{2\pi}{5}\)
C \(\frac{5\pi}{18}\)
D \(\frac{7\pi}{20}\)
Explanation opens after your attempt
Correct Answer
A. \(\frac{3\pi}{10}\)
Step 1
Concept
\(54^\circ\times\frac{\pi}{180}=\frac{3\pi}{10}\). Use \(\frac{\pi}{180}\) when converting degrees to radians.
Step 2
Why this answer is correct
The correct answer is A. \(\frac{3\pi}{10}\). \(54^\circ\times\frac{\pi}{180}=\frac{3\pi}{10}\). Use \(\frac{\pi}{180}\) when converting degrees to radians.
Step 3
Exam Tip
\(54^\circ\times\frac{\pi}{180}=\frac{3\pi}{10}\) होता है। डिग्री से रेडियन में जाने पर \(\frac{\pi}{180}\) लगाएं।
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\(\frac{13\pi}{6}\) किस छोटे धनात्मक कोण के साथ सहप्रारंभी है?
\(\frac{13\pi}{6}\) is coterminal with which smaller positive angle?
#trigonometric-functions
#coterminal-angle
#radian-measure
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A \(\frac{\pi}{6}\)
B \(\frac{\pi}{3}\)
C \(\frac{5\pi}{6}\)
D \(\frac{7\pi}{6}\)
Explanation opens after your attempt
Correct Answer
A. \(\frac{\pi}{6}\)
Step 1
Concept
\(\frac{13\pi}{6}-2\pi=\frac{\pi}{6}\). Subtract \(2\pi\) to obtain the principal angle.
Step 2
Why this answer is correct
The correct answer is A. \(\frac{\pi}{6}\). \(\frac{13\pi}{6}-2\pi=\frac{\pi}{6}\). Subtract \(2\pi\) to obtain the principal angle.
Step 3
Exam Tip
\(\frac{13\pi}{6}-2\pi=\frac{\pi}{6}\) है। \(2\pi\) घटाकर मुख्य कोण प्राप्त करें।
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यदि \(\theta=110^\circ\) है तो \(\theta\) के सभी सहप्रारंभी कोणों का सामान्य रूप क्या है?
If \(\theta=110^\circ\) then what is the general form of all coterminal angles of \(\theta\)?
#trigonometric-functions
#general-coterminal-angle
#degree-measure
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A \(110^\circ+180^\circ k\)
B \(110^\circ+360^\circ k\)
C \(110^\circ-90^\circ k\)
D \(110^\circ+90^\circ k\)
Explanation opens after your attempt
Correct Answer
B. \(110^\circ+360^\circ k\)
Step 1
Concept
In degrees coterminal angles are obtained by adding multiples of \(360^\circ\). So the form is \(110^\circ+360^\circ k\).
Step 2
Why this answer is correct
The correct answer is B. \(110^\circ+360^\circ k\). In degrees coterminal angles are obtained by adding multiples of \(360^\circ\). So the form is \(110^\circ+360^\circ k\).
Step 3
Exam Tip
डिग्री में सहप्रारंभी कोण \(360^\circ\) के गुणज जोड़कर मिलते हैं। इसलिए रूप \(110^\circ+360^\circ k\) है।
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\(\frac{\pi}{9}\) रेडियन कितने डिग्री के बराबर है?
How many degrees are equal to \(\frac{\pi}{9}\) radians?
#trigonometric-functions
#radian-to-degree
#angle-conversion
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A \(10^\circ\)
B \(20^\circ\)
C \(30^\circ\)
D \(40^\circ\)
Explanation opens after your attempt
Correct Answer
B. \(20^\circ\)
Step 1
Concept
\(\frac{\pi}{9}\times\frac{180^\circ}{\pi}=20^\circ\). Multiply by \(\frac{180}{\pi}\) to convert radians into degrees.
Step 2
Why this answer is correct
The correct answer is B. \(20^\circ\). \(\frac{\pi}{9}\times\frac{180^\circ}{\pi}=20^\circ\). Multiply by \(\frac{180}{\pi}\) to convert radians into degrees.
Step 3
Exam Tip
\(\frac{\pi}{9}\times\frac{180^\circ}{\pi}=20^\circ\) है। रेडियन से डिग्री में जाने पर \(\frac{180}{\pi}\) से गुणा करें।
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\(72^\circ\) का रेडियन माप क्या है?
What is the radian measure of \(72^\circ\)?
#trigonometric-functions
#degree-to-radian
#angle-conversion
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A \(\frac{\pi}{5}\)
B \(\frac{2\pi}{5}\)
C \(\frac{3\pi}{5}\)
D \(\frac{4\pi}{5}\)
Explanation opens after your attempt
Correct Answer
B. \(\frac{2\pi}{5}\)
Step 1
Concept
\(72^\circ\times\frac{\pi}{180}=\frac{2\pi}{5}\). Divide (72) and (180) by (36) while simplifying.
Step 2
Why this answer is correct
The correct answer is B. \(\frac{2\pi}{5}\). \(72^\circ\times\frac{\pi}{180}=\frac{2\pi}{5}\). Divide (72) and (180) by (36) while simplifying.
Step 3
Exam Tip
\(72^\circ\times\frac{\pi}{180}=\frac{2\pi}{5}\) होता है। सरलीकरण में (72) और (180) को (36) से भाग दें।
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यदि चाप की लंबाई \(8\pi\) सेमी और त्रिज्या (16) सेमी है तो केंद्रीय कोण क्या है?
If the arc length is \(8\pi\) cm and the radius is (16) cm then what is the central angle?
#trigonometric-functions
#arc-length
#central-angle
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A \(\frac{\pi}{4}\)
B \(\frac{\pi}{2}\)
C \(\pi\)
D \(\frac{3\pi}{2}\)
Explanation opens after your attempt
Correct Answer
B. \(\frac{\pi}{2}\)
Step 1
Concept
\(\theta=\frac{s}{r}=\frac{8\pi}{16}=\frac{\pi}{2}\). Apply the arc length formula in reverse.
Step 2
Why this answer is correct
The correct answer is B. \(\frac{\pi}{2}\). \(\theta=\frac{s}{r}=\frac{8\pi}{16}=\frac{\pi}{2}\). Apply the arc length formula in reverse.
Step 3
Exam Tip
\(\theta=\frac{s}{r}=\frac{8\pi}{16}=\frac{\pi}{2}\) है। चाप लंबाई सूत्र को उल्टा लगाएं।
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त्रिज्या (9) सेमी और क्षेत्रफल \(45\pi\) वर्ग सेमी वाले त्रिज्यखंड का केंद्रीय कोण क्या है?
What is the central angle of a sector with radius (9) cm and area \(45\pi\) sq cm?
#trigonometric-functions
#sector-area
#central-angle
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A \(\frac{8\pi}{9}\)
B \(\frac{10\pi}{9}\)
C \(\frac{11\pi}{9}\)
D \(\frac{5\pi}{3}\)
Explanation opens after your attempt
Correct Answer
B. \(\frac{10\pi}{9}\)
Step 1
Concept
Put \(\frac{1}{2}r^2\theta=45\pi\). From \(\frac{81}{2}\theta=45\pi\) we get \(\theta=\frac{10\pi}{9}\).
Step 2
Why this answer is correct
The correct answer is B. \(\frac{10\pi}{9}\). Put \(\frac{1}{2}r^2\theta=45\pi\). From \(\frac{81}{2}\theta=45\pi\) we get \(\theta=\frac{10\pi}{9}\).
Step 3
Exam Tip
\(\frac{1}{2}r^2\theta=45\pi\) रखें। \(\frac{81}{2}\theta=45\pi\) से \(\theta=\frac{10\pi}{9}\) मिलता है।
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घंटे की सुई (3) घंटे (20) मिनट में कितने डिग्री घूमती है?
Through how many degrees does the hour hand turn in (3) hours (20) minutes?
#trigonometric-functions
#clock-angle
#hour-hand
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A \(90^\circ\)
B \(100^\circ\)
C \(110^\circ\)
D \(120^\circ\)
Explanation opens after your attempt
Correct Answer
B. \(100^\circ\)
Step 1
Concept
The hour hand turns \(30^\circ\) in (1) hour. In \(\frac{10}{3}\) hours the angle is \(100^\circ\).
Step 2
Why this answer is correct
The correct answer is B. \(100^\circ\). The hour hand turns \(30^\circ\) in (1) hour. In \(\frac{10}{3}\) hours the angle is \(100^\circ\).
Step 3
Exam Tip
घंटे की सुई (1) घंटे में \(30^\circ\) घूमती है। \(\frac{10}{3}\) घंटे में कोण \(100^\circ\) होगा।
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मिनट सुई (7.5) मिनट में कितने रेडियन घूमती है?
Through how many radians does the minute hand turn in (7.5) minutes?
#trigonometric-functions
#clock-angle
#minute-hand
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A \(\frac{\pi}{6}\)
B \(\frac{\pi}{4}\)
C \(\frac{\pi}{3}\)
D \(\frac{\pi}{2}\)
Explanation opens after your attempt
Correct Answer
B. \(\frac{\pi}{4}\)
Step 1
Concept
It turns \(2\pi\) radians in (60) minutes. In (7.5) minutes it turns \(\frac{7.5}{60}\times2\pi=\frac{\pi}{4}\).
Step 2
Why this answer is correct
The correct answer is B. \(\frac{\pi}{4}\). It turns \(2\pi\) radians in (60) minutes. In (7.5) minutes it turns \(\frac{7.5}{60}\times2\pi=\frac{\pi}{4}\).
Step 3
Exam Tip
(60) मिनट में \(2\pi\) रेडियन घूमती है। (7.5) मिनट में \(\frac{7.5}{60}\times2\pi=\frac{\pi}{4}\) है।
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कोण \(-\frac{23\pi}{6}\) का (0) और \(2\pi\) के बीच सहप्रारंभी कोण क्या है?
What is the coterminal angle of \(-\frac{23\pi}{6}\) between (0) and \(2\pi\)?
#trigonometric-functions
#coterminal-angle
#radian-measure
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A \(\frac{\pi}{6}\)
B \(\frac{\pi}{3}\)
C \(\frac{5\pi}{6}\)
D \(\frac{11\pi}{6}\)
Explanation opens after your attempt
Correct Answer
A. \(\frac{\pi}{6}\)
Step 1
Concept
\(-\frac{23\pi}{6}+4\pi=\frac{\pi}{6}\). Add multiples of \(2\pi\) to a negative radian angle.
Step 2
Why this answer is correct
The correct answer is A. \(\frac{\pi}{6}\). \(-\frac{23\pi}{6}+4\pi=\frac{\pi}{6}\). Add multiples of \(2\pi\) to a negative radian angle.
Step 3
Exam Tip
\(-\frac{23\pi}{6}+4\pi=\frac{\pi}{6}\) है। नकारात्मक रेडियन कोण में \(2\pi\) के गुणज जोड़ें।
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कोण \(\frac{11\pi}{10}\) का संदर्भ कोण क्या है?
What is the reference angle of \(\frac{11\pi}{10}\)?
#trigonometric-functions
#reference-angle
#radian-measure
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A \(\frac{\pi}{20}\)
B \(\frac{\pi}{10}\)
C \(\frac{3\pi}{10}\)
D \(\frac{9\pi}{10}\)
Explanation opens after your attempt
Correct Answer
B. \(\frac{\pi}{10}\)
Step 1
Concept
\(\frac{11\pi}{10}\) lies in the third quadrant. The reference angle is \(\frac{11\pi}{10}-\pi=\frac{\pi}{10}\).
Step 2
Why this answer is correct
The correct answer is B. \(\frac{\pi}{10}\). \(\frac{11\pi}{10}\) lies in the third quadrant. The reference angle is \(\frac{11\pi}{10}-\pi=\frac{\pi}{10}\).
Step 3
Exam Tip
\(\frac{11\pi}{10}\) तृतीय चतुर्थांश में है। संदर्भ कोण \(\frac{11\pi}{10}-\pi=\frac{\pi}{10}\) है।
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किसी कोण का संपूरक कोण उसके दुगुने से \(40^\circ\) कम है। वह कोण क्या है?
The supplement of an angle is \(40^\circ\) less than twice the angle. What is the angle?
#trigonometric-functions
#supplementary-angles
#angle-equation
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A \(\frac{200^\circ}{3}\)
B \(\frac{210^\circ}{3}\)
C \(\frac{220^\circ}{3}\)
D \(\frac{230^\circ}{3}\)
Explanation opens after your attempt
Correct Answer
C. \(\frac{220^\circ}{3}\)
Step 1
Concept
If the angle is (x) then \(180^\circ-x=2x-40^\circ\). This gives \(x=\frac{220^\circ}{3}\).
Step 2
Why this answer is correct
The correct answer is C. \(\frac{220^\circ}{3}\). If the angle is (x) then \(180^\circ-x=2x-40^\circ\). This gives \(x=\frac{220^\circ}{3}\).
Step 3
Exam Tip
यदि कोण (x) है तो \(180^\circ-x=2x-40^\circ\) होगा। इससे \(x=\frac{220^\circ}{3}\) मिलता है।
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कोण \(12^\circ30'\) का रेडियन माप क्या है?
What is the radian measure of \(12^\circ30'\)?
#trigonometric-functions
#dms-to-radians
#angle-conversion
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A \(\frac{5\pi}{72}\)
B \(\frac{7\pi}{72}\)
C \(\frac{11\pi}{144}\)
D \(\frac{13\pi}{144}\)
Explanation opens after your attempt
Correct Answer
A. \(\frac{5\pi}{72}\)
Step 1
Concept
\(12^\circ30'=12.5^\circ=\frac{25}{2}^\circ\). In radians it is \(\frac{25}{2}\times\frac{\pi}{180}=\frac{5\pi}{72}\).
Step 2
Why this answer is correct
The correct answer is A. \(\frac{5\pi}{72}\). \(12^\circ30'=12.5^\circ=\frac{25}{2}^\circ\). In radians it is \(\frac{25}{2}\times\frac{\pi}{180}=\frac{5\pi}{72}\).
Step 3
Exam Tip
\(12^\circ30'=12.5^\circ=\frac{25}{2}^\circ\) होता है। रेडियन में \(\frac{25}{2}\times\frac{\pi}{180}=\frac{5\pi}{72}\) है।
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\(\frac{7\pi}{2}\) रेडियन कितने पूर्ण चक्करों के बराबर है?
\(\frac{7\pi}{2}\) radians is equal to how many revolutions?
#trigonometric-functions
#radian-to-revolution
#angle-measure
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A \(\frac{5}{4}\)
B \(\frac{3}{2}\)
C \(\frac{7}{4}\)
D (2)
Explanation opens after your attempt
Correct Answer
C. \(\frac{7}{4}\)
Step 1
Concept
One revolution is \(2\pi\) radians. \(\frac{7\pi}{2}\div2\pi=\frac{7}{4}\) revolutions.
Step 2
Why this answer is correct
The correct answer is C. \(\frac{7}{4}\). One revolution is \(2\pi\) radians. \(\frac{7\pi}{2}\div2\pi=\frac{7}{4}\) revolutions.
Step 3
Exam Tip
एक चक्कर \(2\pi\) रेडियन होता है। \(\frac{7\pi}{2}\div2\pi=\frac{7}{4}\) चक्कर।
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यदि \(\theta=-315^\circ\) है तो \(0^\circ\le\theta<360^\circ\) में इसका सहप्रारंभी कोण क्या होगा?
If \(\theta=-315^\circ\) then what is its coterminal angle in \(0^\circ\le\theta<360^\circ\)?
#trigonometric-functions
#coterminal-angle
#principal-angle
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A \(30^\circ\)
B \(45^\circ\)
C \(60^\circ\)
D \(75^\circ\)
Explanation opens after your attempt
Correct Answer
B. \(45^\circ\)
Step 1
Concept
\(-315^\circ+360^\circ=45^\circ\). Add \(360^\circ\) to bring it into the given interval.
Step 2
Why this answer is correct
The correct answer is B. \(45^\circ\). \(-315^\circ+360^\circ=45^\circ\). Add \(360^\circ\) to bring it into the given interval.
Step 3
Exam Tip
\(-315^\circ+360^\circ=45^\circ\) है। दिए गए अंतराल में लाने के लिए \(360^\circ\) जोड़ें।
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(4) रेडियन का डिग्री माप लगभग कितना है?
What is the approximate degree measure of (4) radians?
#trigonometric-functions
#radian-to-degree
#approximation
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A \(206.3^\circ\)
B \(218.6^\circ\)
C \(229.2^\circ\)
D \(240.5^\circ\)
Explanation opens after your attempt
Correct Answer
C. \(229.2^\circ\)
Step 1
Concept
(4) radians \(=4\times\frac{180^\circ}{\pi}\approx229.2^\circ\). Use \(\pi\approx3.14\) for approximation.
Step 2
Why this answer is correct
The correct answer is C. \(229.2^\circ\). (4) radians \(=4\times\frac{180^\circ}{\pi}\approx229.2^\circ\). Use \(\pi\approx3.14\) for approximation.
Step 3
Exam Tip
(4) रेडियन \(=4\times\frac{180^\circ}{\pi}\approx229.2^\circ\) है। अनुमान में \(\pi\approx3.14\) रखें।
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किसी चाप की लंबाई समान रखते हुए त्रिज्या दुगुनी कर दी जाती है। यदि पहले कोण \(\frac{3\pi}{5}\) था तो नया कोण क्या होगा?
Keeping the arc length same the radius is doubled. If the earlier angle was \(\frac{3\pi}{5}\) then what will be the new angle?
#trigonometric-functions
#arc-length
#proportional-reasoning
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A \(\frac{3\pi}{10}\)
B \(\frac{3\pi}{5}\)
C \(\frac{6\pi}{5}\)
D \(\frac{9\pi}{10}\)
Explanation opens after your attempt
Correct Answer
A. \(\frac{3\pi}{10}\)
Step 1
Concept
For the same arc length \(\theta\) is inversely proportional to radius. When radius doubles the angle becomes half as \(\frac{3\pi}{10}\).
Step 2
Why this answer is correct
The correct answer is A. \(\frac{3\pi}{10}\). For the same arc length \(\theta\) is inversely proportional to radius. When radius doubles the angle becomes half as \(\frac{3\pi}{10}\).
Step 3
Exam Tip
समान चाप लंबाई के लिए \(\theta\) त्रिज्या के व्युत्क्रमानुपाती है। त्रिज्या दुगुनी होने पर कोण आधा होकर \(\frac{3\pi}{10}\) होगा।
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पूर्ण चक्कर के \(\frac{3}{8}\) भाग का रेडियन माप क्या है?
What is the radian measure of \(\frac{3}{8}\) of a complete revolution?
#trigonometric-functions
#revolution-to-radian
#angle-measure
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A \(\frac{\pi}{2}\)
B \(\frac{2\pi}{3}\)
C \(\frac{3\pi}{4}\)
D \(\frac{5\pi}{4}\)
Explanation opens after your attempt
Correct Answer
C. \(\frac{3\pi}{4}\)
Step 1
Concept
A complete revolution is \(2\pi\) radians. \(\frac{3}{8}\times2\pi=\frac{3\pi}{4}\).
Step 2
Why this answer is correct
The correct answer is C. \(\frac{3\pi}{4}\). A complete revolution is \(2\pi\) radians. \(\frac{3}{8}\times2\pi=\frac{3\pi}{4}\).
Step 3
Exam Tip
पूर्ण चक्कर \(2\pi\) रेडियन है। \(\frac{3}{8}\times2\pi=\frac{3\pi}{4}\) होता है।
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कोण \(1490^\circ\) का सबसे छोटा धनात्मक सहप्रारंभी कोण क्या है?
What is the least positive coterminal angle of \(1490^\circ\)?
#trigonometric-functions
#coterminal-angle
#degree-measure
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A \(40^\circ\)
B \(50^\circ\)
C \(60^\circ\)
D \(70^\circ\)
Explanation opens after your attempt
Correct Answer
B. \(50^\circ\)
Step 1
Concept
\(1490^\circ-1440^\circ=50^\circ\). Subtract the largest possible multiple of \(360^\circ\).
Step 2
Why this answer is correct
The correct answer is B. \(50^\circ\). \(1490^\circ-1440^\circ=50^\circ\). Subtract the largest possible multiple of \(360^\circ\).
Step 3
Exam Tip
\(1490^\circ-1440^\circ=50^\circ\) है। \(360^\circ\) के अधिकतम संभव गुणज को घटाएं।
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यदि कोई कोण तृतीय चतुर्थांश में है और उसका संदर्भ कोण \(\frac{\pi}{7}\) है तो वह कोण क्या है?
If an angle lies in the third quadrant and its reference angle is \(\frac{\pi}{7}\) then what is the angle?
#trigonometric-functions
#reference-angle
#quadrant
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A \(\frac{6\pi}{7}\)
B \(\frac{8\pi}{7}\)
C \(\frac{9\pi}{7}\)
D \(\frac{13\pi}{7}\)
Explanation opens after your attempt
Correct Answer
B. \(\frac{8\pi}{7}\)
Step 1
Concept
In the third quadrant the angle is \(\pi+\) reference angle. Hence \(\pi+\frac{\pi}{7}=\frac{8\pi}{7}\).
Step 2
Why this answer is correct
The correct answer is B. \(\frac{8\pi}{7}\). In the third quadrant the angle is \(\pi+\) reference angle. Hence \(\pi+\frac{\pi}{7}=\frac{8\pi}{7}\).
Step 3
Exam Tip
तृतीय चतुर्थांश में कोण \(\pi+\) संदर्भ कोण होता है। इसलिए \(\pi+\frac{\pi}{7}=\frac{8\pi}{7}\) है।
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निम्न में से कौन सी जोड़ी सहप्रारंभी कोणों की है?
Which of the following pairs consists of coterminal angles?
#trigonometric-functions
#coterminal-angle
#angle-pair
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A \(45^\circ\) और \(405^\circ\) / \(45^\circ\) and \(405^\circ\)
B \(70^\circ\) और \(790^\circ\) / \(70^\circ\) and \(790^\circ\)
C \(120^\circ\) और \(420^\circ\) / \(120^\circ\) and \(420^\circ\)
D \(150^\circ\) और \(480^\circ\) / \(150^\circ\) and \(480^\circ\)
Explanation opens after your attempt
Correct Answer
A. \(45^\circ\) और \(405^\circ\) / \(45^\circ\) and \(405^\circ\)
Step 1
Concept
\(405^\circ-45^\circ=360^\circ\) so they are coterminal. The difference must be a multiple of \(360^\circ\).
Step 2
Why this answer is correct
The correct answer is A. \(45^\circ\) और \(405^\circ\) / \(45^\circ\) and \(405^\circ\). \(405^\circ-45^\circ=360^\circ\) so they are coterminal. The difference must be a multiple of \(360^\circ\).
Step 3
Exam Tip
\(405^\circ-45^\circ=360^\circ\) है इसलिए दोनों सहप्रारंभी हैं। अंतर \(360^\circ\) का गुणज होना चाहिए।
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(1) रेडियन की सही ज्यामितीय व्याख्या कौन सी है?
Which is the correct geometrical interpretation of (1) radian?
#trigonometric-functions
#one-radian
#definition
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A जब चाप लंबाई त्रिज्या के बराबर हो / When arc length equals radius
B जब चाप लंबाई व्यास के बराबर हो / When arc length equals diameter
C जब कोण \(90^\circ\) हो / When the angle is \(90^\circ\)
D जब चाप लंबाई परिधि के बराबर हो / When arc length equals circumference
Explanation opens after your attempt
Correct Answer
A. जब चाप लंबाई त्रिज्या के बराबर हो / When arc length equals radius
Step 1
Concept
(1) radian is formed when (s=r). For definition based questions remember \(s=r\theta\).
Step 2
Why this answer is correct
The correct answer is A. जब चाप लंबाई त्रिज्या के बराबर हो / When arc length equals radius. (1) radian is formed when (s=r). For definition based questions remember \(s=r\theta\).
Step 3
Exam Tip
(1) रेडियन तब बनता है जब (s=r) हो। परिभाषा आधारित प्रश्नों में \(s=r\theta\) को याद रखें.
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त्रिज्या (63) मीटर वाले वृत्ताकार पथ पर \(40^\circ\) केंद्रीय कोण के बराबर चली दूरी क्या है?
On a circular track of radius (63) m what is the distance covered for a central angle of \(40^\circ\)?
#trigonometric-functions
#arc-length
#degree-to-radian
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A \(12\pi\) मीटर / \(12\pi\) m
B \(14\pi\) मीटर / \(14\pi\) m
C \(16\pi\) मीटर / \(16\pi\) m
D \(18\pi\) मीटर / \(18\pi\) m
Explanation opens after your attempt
Correct Answer
B. \(14\pi\) मीटर / \(14\pi\) m
Step 1
Concept
\(40^\circ=\frac{2\pi}{9}\) radians. The distance is \(s=63\times\frac{2\pi}{9}=14\pi\) m.
Step 2
Why this answer is correct
The correct answer is B. \(14\pi\) मीटर / \(14\pi\) m. \(40^\circ=\frac{2\pi}{9}\) radians. The distance is \(s=63\times\frac{2\pi}{9}=14\pi\) m.
Step 3
Exam Tip
\(40^\circ=\frac{2\pi}{9}\) रेडियन है। दूरी \(s=63\times\frac{2\pi}{9}=14\pi\) मीटर होगी।
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