घड़ी में (11:54) पर घंटे और मिनट की सुइयों के बीच छोटा कोण क्या है?
What is the smaller angle between the hour and minute hands at (11:54)?
#trigonometric-functions
#clock-angle
#degree-measure
A \(27^\circ\)
B \(30^\circ\)
C \(33^\circ\)
D \(36^\circ\)
Explanation opens after your attempt
Correct Answer
C. \(33^\circ\)
Step 1
Concept
The minute hand is at \(324^\circ\) and the hour hand is at \(357^\circ\). The smaller difference is \(33^\circ\).
Step 2
Why this answer is correct
The correct answer is C. \(33^\circ\). The minute hand is at \(324^\circ\) and the hour hand is at \(357^\circ\). The smaller difference is \(33^\circ\).
Step 3
Exam Tip
मिनट सुई \(324^\circ\) पर और घंटे की सुई \(357^\circ\) पर होती है। छोटा अंतर \(33^\circ\) है।
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एक पहिया (11) पूर्ण चक्कर और फिर \(\frac{2\pi}{3}\) रेडियन घूमता है। कुल कोण डिग्री में कितना है?
A wheel turns (11) complete revolutions and then \(\frac{2\pi}{3}\) radians. What is the total angle in degrees?
#trigonometric-functions
#revolutions
#degree-measure
A \(3960^\circ\)
B \(4020^\circ\)
C \(4080^\circ\)
D \(4140^\circ\)
Explanation opens after your attempt
Correct Answer
C. \(4080^\circ\)
Step 1
Concept
(11) revolutions are \(3960^\circ\) and \(\frac{2\pi}{3}=120^\circ\). The total angle is \(4080^\circ\).
Step 2
Why this answer is correct
The correct answer is C. \(4080^\circ\). (11) revolutions are \(3960^\circ\) and \(\frac{2\pi}{3}=120^\circ\). The total angle is \(4080^\circ\).
Step 3
Exam Tip
(11) चक्कर \(3960^\circ\) और \(\frac{2\pi}{3}=120^\circ\) है। कुल कोण \(4080^\circ\) होगा।
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कोण \(-1025^\circ\) का सबसे छोटा धनात्मक सहप्रारंभी कोण क्या है?
What is the least positive coterminal angle of \(-1025^\circ\)?
#trigonometric-functions
#coterminal-angle
#degree-measure
A \(45^\circ\)
B \(50^\circ\)
C \(55^\circ\)
D \(65^\circ\)
Explanation opens after your attempt
Correct Answer
C. \(55^\circ\)
Step 1
Concept
\(-1025^\circ+1080^\circ=55^\circ\). Add multiples of \(360^\circ\) to a large negative angle.
Step 2
Why this answer is correct
The correct answer is C. \(55^\circ\). \(-1025^\circ+1080^\circ=55^\circ\). Add multiples of \(360^\circ\) to a large negative angle.
Step 3
Exam Tip
\(-1025^\circ+1080^\circ=55^\circ\) है। नकारात्मक बड़े कोण में \(360^\circ\) के गुणज जोड़ें।
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घड़ी में (7:38) पर घंटे और मिनट की सुइयों के बीच छोटा कोण क्या है?
What is the smaller angle between the hour and minute hands at (7:38)?
#trigonometric-functions
#clock-angle
#degree-measure
A \(1^\circ\)
B \(2^\circ\)
C \(4^\circ\)
D \(6^\circ\)
Explanation opens after your attempt
Correct Answer
A. \(1^\circ\)
Step 1
Concept
The minute hand is at \(228^\circ\) and the hour hand is at \(229^\circ\). The smaller difference is \(1^\circ\).
Step 2
Why this answer is correct
The correct answer is A. \(1^\circ\). The minute hand is at \(228^\circ\) and the hour hand is at \(229^\circ\). The smaller difference is \(1^\circ\).
Step 3
Exam Tip
मिनट सुई \(228^\circ\) पर और घंटे की सुई \(229^\circ\) पर होती है। छोटा अंतर \(1^\circ\) 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
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 \(\theta=110^\circ\) 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
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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लगभग (1) रेडियन कितने डिग्री के बराबर होता है?
Approximately (1) radian is equal to how many degrees?
#trigonometric-functions
#one-radian
#degree-measure
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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कोण \(1280^\circ\) का संदर्भ कोण क्या है?
What is the reference angle of \(1280^\circ\)?
#trigonometric-functions
#reference-angle
#degree-measure
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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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
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 \(920^\circ\) का सबसे छोटा धनात्मक सहप्रारंभी कोण क्या है?
What is the least positive coterminal angle of \(920^\circ\)?
#trigonometric-functions
#coterminal-angle
#degree-measure
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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\(\frac{3\pi}{2}\) रेडियन कितने डिग्री के बराबर है?
\(\frac{3\pi}{2}\) radians is equal to how many degrees?
#trigonometry
#angles
#degree-measure
A \(180^\circ\)
B \(270^\circ\)
C \(300^\circ\)
D \(360^\circ\)
Explanation opens after your attempt
Correct Answer
B. \(270^\circ\)
Step 1
Concept
\(\frac{3\pi}{2}\times\frac{180^\circ}{\pi}=270^\circ\). The numerator (3) makes the final value three times \(90^\circ\).
Step 2
Why this answer is correct
The correct answer is B. \(270^\circ\). \(\frac{3\pi}{2}\times\frac{180^\circ}{\pi}=270^\circ\). The numerator (3) makes the final value three times \(90^\circ\).
Step 3
Exam Tip
\(\frac{3\pi}{2}\times\frac{180^\circ}{\pi}=270^\circ\) होता है। ऊपर का (3) अंतिम मान को तीन गुना करता है।
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