In this formula (s) represents arc length. Knowing the symbols helps in applying the formula correctly.
Step 2
Why this answer is correct
The correct answer is B. चाप की लंबाई / Arc length. In this formula (s) represents arc length. Knowing the symbols helps in applying the formula correctly.
Step 3
Exam Tip
इस सूत्र में (s) चाप की लंबाई को दर्शाता है। प्रतीकों का अर्थ याद रखने से सूत्र सही लगता है।
In this formula (r) represents the radius of the circle. In radian questions distinguish radius and arc length.
Step 2
Why this answer is correct
The correct answer is C. त्रिज्या / Radius. In this formula (r) represents the radius of the circle. In radian questions distinguish radius and arc length.
Step 3
Exam Tip
इस सूत्र में (r) वृत्त की त्रिज्या को दर्शाता है। रेडियन वाले प्रश्नों में त्रिज्या और चाप अलग पहचानें।
To convert degrees into radians multiply by \(\frac{\pi}{180^\circ}\). If conversion direction reverses the factor also reverses.
Step 2
Why this answer is correct
The correct answer is D. \(\frac{\pi}{180^\circ}\). To convert degrees into radians multiply by \(\frac{\pi}{180^\circ}\). If conversion direction reverses the factor also reverses.
Step 3
Exam Tip
डिग्री से रेडियन में बदलने के लिए \(\frac{\pi}{180^\circ}\) से गुणा करते हैं। दिशा उलटी हो तो गुणक भी उलटा होता है।
To convert radians into degrees multiply by \(\frac{180^\circ}{\pi}\). Cancel \(\pi\) first and then calculate.
Step 2
Why this answer is correct
The correct answer is A. \(\frac{180^\circ}{\pi}\). To convert radians into degrees multiply by \(\frac{180^\circ}{\pi}\). Cancel \(\pi\) first and then calculate.
Step 3
Exam Tip
रेडियन से डिग्री में बदलने के लिए \(\frac{180^\circ}{\pi}\) से गुणा करते हैं। पहले \(\pi\) को काटकर गणना करें।
\(330^\circ\times\frac{\pi}{180^\circ}=\frac{11\pi}{6}\). You can also remember it using \(30^\circ=\frac{\pi}{6}\).
Step 2
Why this answer is correct
The correct answer is A. \(\frac{11\pi}{6}\). \(330^\circ\times\frac{\pi}{180^\circ}=\frac{11\pi}{6}\). You can also remember it using \(30^\circ=\frac{\pi}{6}\).
Step 3
Exam Tip
\(330^\circ\times\frac{\pi}{180^\circ}=\frac{11\pi}{6}\) होता है। \(30^\circ=\frac{\pi}{6}\) से भी याद रख सकते हैं।
\(\frac{11\pi}{6}\times\frac{180^\circ}{\pi}=330^\circ\). After canceling \(\pi\), calculate \(11\times30^\circ\).
Step 2
Why this answer is correct
The correct answer is B. \(330^\circ\). \(\frac{11\pi}{6}\times\frac{180^\circ}{\pi}=330^\circ\). After canceling \(\pi\), calculate \(11\times30^\circ\).
Step 3
Exam Tip
\(\frac{11\pi}{6}\times\frac{180^\circ}{\pi}=330^\circ\) होता है। \(\pi\) कटने के बाद \(11\times30^\circ\) करें।
\(1^\circ=\frac{\pi}{180}\approx0.01745\) radian. A small degree angle has a small radian value.
Step 2
Why this answer is correct
The correct answer is A. (0.01745) रेडियन / (0.01745) radian. \(1^\circ=\frac{\pi}{180}\approx0.01745\) radian. A small degree angle has a small radian value.
Step 3
Exam Tip
\(1^\circ=\frac{\pi}{180}\approx0.01745\) रेडियन होता है। छोटे डिग्री कोण का रेडियन मान छोटा होता है।
\(35^\circ\) lies between \(0^\circ\) and \(90^\circ\), so it is in the first quadrant. Identify quadrants using boundary angles.
Step 2
Why this answer is correct
The correct answer is B. \(35^\circ\). \(35^\circ\) lies between \(0^\circ\) and \(90^\circ\), so it is in the first quadrant. Identify quadrants using boundary angles.
Step 3
Exam Tip
\(35^\circ\), \(0^\circ\) और \(90^\circ\) के बीच है इसलिए पहले चतुर्थांश में है। सीमा कोणों से चतुर्थांश पहचानें।
\(145^\circ\) lies between \(90^\circ\) and \(180^\circ\), so it is in the second quadrant. First check the range of the angle.
Step 2
Why this answer is correct
The correct answer is C. \(145^\circ\). \(145^\circ\) lies between \(90^\circ\) and \(180^\circ\), so it is in the second quadrant. First check the range of the angle.
Step 3
Exam Tip
\(145^\circ\), \(90^\circ\) और \(180^\circ\) के बीच है इसलिए दूसरे चतुर्थांश में है। कोण की स्थिति पहले दायरा देखकर तय करें।
\(235^\circ\) lies between \(180^\circ\) and \(270^\circ\), so it is in the third quadrant. Remember the range of the third quadrant.
Step 2
Why this answer is correct
The correct answer is D. \(235^\circ\). \(235^\circ\) lies between \(180^\circ\) and \(270^\circ\), so it is in the third quadrant. Remember the range of the third quadrant.
Step 3
Exam Tip
\(235^\circ\), \(180^\circ\) और \(270^\circ\) के बीच है इसलिए तीसरे चतुर्थांश में है। तीसरे चतुर्थांश की सीमा याद रखें।
\(320^\circ\) lies between \(270^\circ\) and \(360^\circ\), so it is in the fourth quadrant. The fourth quadrant comes after \(270^\circ\).
Step 2
Why this answer is correct
The correct answer is A. \(320^\circ\). \(320^\circ\) lies between \(270^\circ\) and \(360^\circ\), so it is in the fourth quadrant. The fourth quadrant comes after \(270^\circ\).
Step 3
Exam Tip
\(320^\circ\), \(270^\circ\) और \(360^\circ\) के बीच है इसलिए चौथे चतुर्थांश में है। \(270^\circ\) के बाद चौथा चतुर्थांश आता है।
At \(180^\circ\), the terminal side lies on the negative (x)-axis. Angles on axes do not belong to any quadrant.
Step 2
Why this answer is correct
The correct answer is B. ऋणात्मक (x)-अक्ष पर / On negative (x)-axis. At \(180^\circ\), the terminal side lies on the negative (x)-axis. Angles on axes do not belong to any quadrant.
Step 3
Exam Tip
\(180^\circ\) पर अंतिम भुजा ऋणात्मक (x)-अक्ष पर होती है। अक्षों पर स्थित कोण किसी चतुर्थांश में नहीं आते।
At \(270^\circ\), the terminal side lies on the negative (y)-axis. Remember axial angles separately.
Step 2
Why this answer is correct
The correct answer is C. ऋणात्मक (y)-अक्ष पर / On negative (y)-axis. At \(270^\circ\), the terminal side lies on the negative (y)-axis. Remember axial angles separately.
Step 3
Exam Tip
\(270^\circ\) पर अंतिम भुजा ऋणात्मक (y)-अक्ष पर होती है। अक्षीय कोणों को अलग से याद रखें।
At \(90^\circ\), the terminal side lies on the positive (y)-axis. In standard position anticlockwise \(90^\circ\) goes upward.
Step 2
Why this answer is correct
The correct answer is D. धनात्मक (y)-अक्ष पर / On positive (y)-axis. At \(90^\circ\), the terminal side lies on the positive (y)-axis. In standard position anticlockwise \(90^\circ\) goes upward.
Step 3
Exam Tip
\(90^\circ\) पर अंतिम भुजा धनात्मक (y)-अक्ष पर होती है। सामान्य स्थिति में वामावर्त \(90^\circ\) ऊपर की ओर जाता है।
At \(0^\circ\), the terminal side stays with the initial side on the positive (x)-axis. A zero angle has no rotation.
Step 2
Why this answer is correct
The correct answer is A. धनात्मक (x)-अक्ष पर / On positive (x)-axis. At \(0^\circ\), the terminal side stays with the initial side on the positive (x)-axis. A zero angle has no rotation.
Step 3
Exam Tip
\(0^\circ\) पर अंतिम भुजा प्रारंभिक भुजा के साथ धनात्मक (x)-अक्ष पर रहती है। शून्य कोण में कोई घूर्णन नहीं होता।
\(-90^\circ\) is clockwise rotation so the terminal side lies on the negative (y)-axis. The negative sign shows direction.
Step 2
Why this answer is correct
The correct answer is B. ऋणात्मक (y)-अक्ष पर / On negative (y)-axis. \(-90^\circ\) is clockwise rotation so the terminal side lies on the negative (y)-axis. The negative sign shows direction.
Step 3
Exam Tip
\(-90^\circ\) दक्षिणावर्त घूर्णन है इसलिए अंतिम भुजा ऋणात्मक (y)-अक्ष पर होती है। ऋणात्मक चिन्ह दिशा बताता है।
\(18'=\frac{18}{60}^\circ=0.30^\circ\), so \(6^\circ18'=6.30^\circ\). Do not treat minutes directly as decimals.
Step 2
Why this answer is correct
The correct answer is C. \(6.30^\circ\). \(18'=\frac{18}{60}^\circ=0.30^\circ\), so \(6^\circ18'=6.30^\circ\). Do not treat minutes directly as decimals.
Step 3
Exam Tip
\(18'=\frac{18}{60}^\circ=0.30^\circ\) इसलिए \(6^\circ18'=6.30^\circ\) है। मिनट को सीधे दशमलव न मानें।
In the second quadrant the reference angle is \(180^\circ-\theta\), so it is \(70^\circ\). A reference angle is always acute.
Step 2
Why this answer is correct
The correct answer is A. \(70^\circ\). In the second quadrant the reference angle is \(180^\circ-\theta\), so it is \(70^\circ\). A reference angle is always acute.
Step 3
Exam Tip
दूसरे चतुर्थांश में संदर्भ कोण \(180^\circ-\theta\) होता है इसलिए \(70^\circ\) मिलता है। संदर्भ कोण हमेशा न्यून कोण होता है।
In the third quadrant the reference angle is \(\theta-180^\circ\), so it is \(70^\circ\). Identify the quadrant first and then apply the rule.
Step 2
Why this answer is correct
The correct answer is B. \(70^\circ\). In the third quadrant the reference angle is \(\theta-180^\circ\), so it is \(70^\circ\). Identify the quadrant first and then apply the rule.
Step 3
Exam Tip
तीसरे चतुर्थांश में संदर्भ कोण \(\theta-180^\circ\) होता है इसलिए \(70^\circ\) मिलता है। पहले चतुर्थांश पहचानें फिर नियम लगाएं।
In the fourth quadrant the reference angle is \(360^\circ-\theta\), so it is \(50^\circ\). Take the smaller angle to the (x)-axis.
Step 2
Why this answer is correct
The correct answer is C. \(50^\circ\). In the fourth quadrant the reference angle is \(360^\circ-\theta\), so it is \(50^\circ\). Take the smaller angle to the (x)-axis.
Step 3
Exam Tip
चौथे चतुर्थांश में संदर्भ कोण \(360^\circ-\theta\) होता है इसलिए \(50^\circ\) मिलता है। अंतिम भुजा से (x)-अक्ष तक का छोटा कोण लें।
In the first quadrant the reference angle is the angle itself, so it is \(28^\circ\). No extra calculation is needed in the first quadrant.
Step 2
Why this answer is correct
The correct answer is D. \(28^\circ\). In the first quadrant the reference angle is the angle itself, so it is \(28^\circ\). No extra calculation is needed in the first quadrant.
Step 3
Exam Tip
पहले चतुर्थांश में संदर्भ कोण वही कोण होता है इसलिए \(28^\circ\) है। पहले चतुर्थांश में अलग गणना की जरूरत नहीं होती।
\(380^\circ-20^\circ=360^\circ\), so they are coterminal angles. If the difference is a multiple of \(360^\circ\), they are coterminal.
Step 2
Why this answer is correct
The correct answer is A. वे सह-अंतिम कोण हैं / They are coterminal angles. \(380^\circ-20^\circ=360^\circ\), so they are coterminal angles. If the difference is a multiple of \(360^\circ\), they are coterminal.
Step 3
Exam Tip
\(380^\circ-20^\circ=360^\circ\) इसलिए दोनों सह-अंतिम कोण हैं। अंतर \(360^\circ\) का गुणज हो तो सह-अंतिम मानें।
B. (2) चक्कर और \(90^\circ\)/(2) revolutions and \(90^\circ\)
Step 1
Concept
\(810^\circ=720^\circ+90^\circ\), so it is (2) complete revolutions and \(90^\circ\) remaining. Separate multiples of \(360^\circ\).
Step 2
Why this answer is correct
The correct answer is B. (2) चक्कर और \(90^\circ\) / (2) revolutions and \(90^\circ\). \(810^\circ=720^\circ+90^\circ\), so it is (2) complete revolutions and \(90^\circ\) remaining. Separate multiples of \(360^\circ\).
Step 3
Exam Tip
\(810^\circ=720^\circ+90^\circ\) इसलिए (2) पूरे चक्कर और \(90^\circ\) शेष हैं। \(360^\circ\) के गुणज अलग करें।
An acute angle lies between \(0^\circ\) and \(90^\circ\), so \(42^\circ\) is correct. Identify angle type using its range.
Step 2
Why this answer is correct
The correct answer is C. \(42^\circ\). An acute angle lies between \(0^\circ\) and \(90^\circ\), so \(42^\circ\) is correct. Identify angle type using its range.
Step 3
Exam Tip
न्यून कोण \(0^\circ\) और \(90^\circ\) के बीच होता है इसलिए \(42^\circ\) सही है। कोण का प्रकार सीमा से पहचानें।
An obtuse angle lies between \(90^\circ\) and \(180^\circ\), so \(132^\circ\) is correct. \(90^\circ\) and \(180^\circ\) themselves are not obtuse angles.
Step 2
Why this answer is correct
The correct answer is D. \(132^\circ\). An obtuse angle lies between \(90^\circ\) and \(180^\circ\), so \(132^\circ\) is correct. \(90^\circ\) and \(180^\circ\) themselves are not obtuse angles.
Step 3
Exam Tip
अधिक कोण \(90^\circ\) और \(180^\circ\) के बीच होता है इसलिए \(132^\circ\) सही है। \(90^\circ\) और \(180^\circ\) खुद अधिक कोण नहीं हैं।
