\(27^\circ 45'=\frac{111}{4}^\circ\), so the radian measure is \(\frac{111\pi}{720}=\frac{37\pi}{240}\). In exams, write minutes as \(\frac{45}{60}^\circ\).
Step 2
Why this answer is correct
The correct answer is B. \(\frac{37\pi}{240}\). \(27^\circ 45'=\frac{111}{4}^\circ\), so the radian measure is \(\frac{111\pi}{720}=\frac{37\pi}{240}\). In exams, write minutes as \(\frac{45}{60}^\circ\).
Step 3
Exam Tip
\(27^\circ 45'=\frac{111}{4}^\circ\), इसलिए रेडियन माप \(\frac{111\pi}{720}=\frac{37\pi}{240}\) है। परीक्षा में मिनट को \(\frac{45}{60}^\circ\) लिखें।
\(2A=40^\circ 30'\) and \(40^\circ 30'-12^\circ 45'=27^\circ 45'\). In exams, remember borrowing while subtracting minutes.
Step 2
Why this answer is correct
The correct answer is C. \(27^\circ 45'\). \(2A=40^\circ 30'\) and \(40^\circ 30'-12^\circ 45'=27^\circ 45'\). In exams, remember borrowing while subtracting minutes.
Step 3
Exam Tip
\(2A=40^\circ 30'\) और \(40^\circ 30'-12^\circ 45'=27^\circ 45'\) है। परीक्षा में मिनट घटाते समय उधार लेना याद रखें।
(5) hours (20) minutes \(=\frac{16}{3}\) hours, which is \(\frac{4}{9}\) of (12) hours. The angle is \(\frac{4}{9}\times2\pi=\frac{8\pi}{9}\).
Step 2
Why this answer is correct
The correct answer is A. \(\frac{8\pi}{9}\). (5) hours (20) minutes \(=\frac{16}{3}\) hours, which is \(\frac{4}{9}\) of (12) hours. The angle is \(\frac{4}{9}\times2\pi=\frac{8\pi}{9}\).
Step 3
Exam Tip
(5) घंटे (20) मिनट \(=\frac{16}{3}\) घंटे है, जो (12) घंटे का \(\frac{4}{9}\) भाग है। कोण \(\frac{4}{9}\times2\pi=\frac{8\pi}{9}\) होगा।
The minute hand moves clockwise, so the angle is \(-\frac{47}{60}\times2\pi=-\frac{47\pi}{30}\). In exams, assign the sign according to direction.
Step 2
Why this answer is correct
The correct answer is B. \(-\frac{47\pi}{30}\). The minute hand moves clockwise, so the angle is \(-\frac{47}{60}\times2\pi=-\frac{47\pi}{30}\). In exams, assign the sign according to direction.
Step 3
Exam Tip
मिनट की सूई दक्षिणावर्त घूमती है, इसलिए कोण \(-\frac{47}{60}\times2\pi=-\frac{47\pi}{30}\) है। परीक्षा में दिशा के अनुसार चिह्न लगाएं।
\(\frac{19\pi}{6}=2\pi+\frac{7\pi}{6}\), so one complete revolution and \(\frac{7\pi}{6}\) remain. In exams, treat \(2\pi\) as one revolution.
Step 2
Why this answer is correct
The correct answer is C. (1) पूर्ण चक्कर और \(\frac{7\pi}{6}\). \(\frac{19\pi}{6}=2\pi+\frac{7\pi}{6}\), so one complete revolution and \(\frac{7\pi}{6}\) remain. In exams, treat \(2\pi\) as one revolution.
Step 3
Exam Tip
\(\frac{19\pi}{6}=2\pi+\frac{7\pi}{6}\), इसलिए एक पूर्ण चक्कर और \(\frac{7\pi}{6}\) बचता है। परीक्षा में \(2\pi\) को एक चक्कर मानें।
The positive principal angle of \(845^\circ\) is \(125^\circ\), so the negative coterminal angle is \(125^\circ-360^\circ=-235^\circ\). In exams, subtract \(360^\circ\) for the negative answer.
Step 2
Why this answer is correct
The correct answer is D. \(-235^\circ\). The positive principal angle of \(845^\circ\) is \(125^\circ\), so the negative coterminal angle is \(125^\circ-360^\circ=-235^\circ\). In exams, subtract \(360^\circ\) for the negative answer.
Step 3
Exam Tip
\(845^\circ\) का धनात्मक प्रधान कोण \(125^\circ\) है, इसलिए ऋणात्मक सह-टर्मिनल कोण \(125^\circ-360^\circ=-235^\circ\) है। परीक्षा में ऋणात्मक उत्तर के लिए \(360^\circ\) घटाएं।
The principal angle of \(-\frac{23\pi}{8}\) is \(\frac{9\pi}{8}\), which lies in the third quadrant. In exams, add \(2\pi\) to a negative angle.
Step 2
Why this answer is correct
The correct answer is B. तीसरा चतुर्थांश / Third quadrant. The principal angle of \(-\frac{23\pi}{8}\) is \(\frac{9\pi}{8}\), which lies in the third quadrant. In exams, add \(2\pi\) to a negative angle.
Step 3
Exam Tip
\(-\frac{23\pi}{8}\) का प्रधान कोण \(\frac{9\pi}{8}\) है, जो तीसरे चतुर्थांश में है। परीक्षा में ऋण कोण में \(2\pi\) जोड़ें।
\(\frac{13\pi}{15}=156^\circ\), which is between \(90^\circ\) and \(180^\circ\). In exams, converting to degrees often makes quadrant identification easier.
Step 2
Why this answer is correct
The correct answer is D. दूसरा चतुर्थांश / Second quadrant. \(\frac{13\pi}{15}=156^\circ\), which is between \(90^\circ\) and \(180^\circ\). In exams, converting to degrees often makes quadrant identification easier.
Step 3
Exam Tip
\(\frac{13\pi}{15}=156^\circ\), जो \(90^\circ\) और \(180^\circ\) के बीच है। परीक्षा में चतुर्थांश तय करने से पहले डिग्री में बदलना आसान होता है।
Supplementary angles sum to \(180^\circ\), so the smaller angle is \(75^\circ=\frac{5\pi}{12}\). In exams, divide \(180^\circ\) in the given ratio.
Step 2
Why this answer is correct
The correct answer is A. \(\frac{5\pi}{12}\). Supplementary angles sum to \(180^\circ\), so the smaller angle is \(75^\circ=\frac{5\pi}{12}\). In exams, divide \(180^\circ\) in the given ratio.
Step 3
Exam Tip
संपूरक कोणों का योग \(180^\circ\) है, इसलिए छोटा कोण \(75^\circ=\frac{5\pi}{12}\) है। परीक्षा में \(180^\circ\) को अनुपात में बांटें।
Complementary angles sum to \(90^\circ\), so the larger angle is \(54^\circ=\frac{3\pi}{10}\). In exams, first find the total parts of the ratio.
Step 2
Why this answer is correct
The correct answer is B. \(\frac{3\pi}{10}\). Complementary angles sum to \(90^\circ\), so the larger angle is \(54^\circ=\frac{3\pi}{10}\). In exams, first find the total parts of the ratio.
Step 3
Exam Tip
पूरक कोणों का योग \(90^\circ\) है, इसलिए बड़ा कोण \(54^\circ=\frac{3\pi}{10}\) है। परीक्षा में अनुपात का कुल भाग पहले निकालें।
The hour hand is at \(85^\circ\) and the minute hand at \(300^\circ\), so the smaller angle is \(145^\circ\). In exams, subtract the larger difference from \(360^\circ\).
Step 2
Why this answer is correct
The correct answer is C. \(145^\circ\). The hour hand is at \(85^\circ\) and the minute hand at \(300^\circ\), so the smaller angle is \(145^\circ\). In exams, subtract the larger difference from \(360^\circ\).
Step 3
Exam Tip
घंटे की सूई \(85^\circ\) और मिनट की सूई \(300^\circ\) पर होगी, इसलिए छोटा कोण \(145^\circ\) है। परीक्षा में बड़े अंतर को \(360^\circ\) से घटाकर छोटा कोण लें।
The hour hand is at \(220^\circ\) and the minute hand at \(120^\circ\), so the difference is \(100^\circ\). In exams, do not forget the extra movement of the hour hand.
Step 2
Why this answer is correct
The correct answer is D. \(100^\circ\). The hour hand is at \(220^\circ\) and the minute hand at \(120^\circ\), so the difference is \(100^\circ\). In exams, do not forget the extra movement of the hour hand.
Step 3
Exam Tip
घंटे की सूई \(220^\circ\) और मिनट की सूई \(120^\circ\) पर होगी, अंतर \(100^\circ\) है। परीक्षा में घंटे की सूई की अतिरिक्त गति न भूलें।
\(\frac{\pi}{3}=60^\circ\), so the new angle is \(45^\circ=\frac{\pi}{4}\). In exams, convert mixed units into one unit.
Step 2
Why this answer is correct
The correct answer is B. \(\frac{\pi}{4}\). \(\frac{\pi}{3}=60^\circ\), so the new angle is \(45^\circ=\frac{\pi}{4}\). In exams, convert mixed units into one unit.
Step 3
Exam Tip
\(\frac{\pi}{3}=60^\circ\), इसलिए नया कोण \(45^\circ=\frac{\pi}{4}\) है। परीक्षा में मिश्रित इकाइयों को एक ही इकाई में बदलें।
For a non-zero angle, the numerical ratio is always \(180/\pi\), not (2). In exams, identify the numerical ratio between degree and radian measures.
Step 2
Why this answer is correct
The correct answer is C. नहीं / No. For a non-zero angle, the numerical ratio is always \(180/\pi\), not (2). In exams, identify the numerical ratio between degree and radian measures.
Step 3
Exam Tip
अशून्य कोण के लिए अनुपात हमेशा \(180/\pi\) होता है, जो (2) नहीं है। परीक्षा में डिग्री और रेडियन के संख्यात्मक अनुपात को पहचानें।
The resulting angle is \(125^\circ-410^\circ=-285^\circ\), which is \(-\frac{19\pi}{12}\) radians. In exams, take anticlockwise as positive and clockwise as negative.
Step 2
Why this answer is correct
The correct answer is D. \(-\frac{19\pi}{12}\). The resulting angle is \(125^\circ-410^\circ=-285^\circ\), which is \(-\frac{19\pi}{12}\) radians. In exams, take anticlockwise as positive and clockwise as negative.
Step 3
Exam Tip
परिणामी कोण \(125^\circ-410^\circ=-285^\circ\) है, जो \(-\frac{19\pi}{12}\) रेडियन है। परीक्षा में वामावर्त को धनात्मक और दक्षिणावर्त को ऋणात्मक लें।
A straight angle is \(180^\circ\), so \(\frac{1}{5}\) is \(36^\circ\) and the total is \(90^\circ\). In exams, translate words step by step.
Step 2
Why this answer is correct
The correct answer is B. \(\frac{\pi}{2}\). A straight angle is \(180^\circ\), so \(\frac{1}{5}\) is \(36^\circ\) and the total is \(90^\circ\). In exams, translate words step by step.
Step 3
Exam Tip
सीधा कोण \(180^\circ\) है, इसलिए \(\frac{1}{5}\) भाग \(36^\circ\) और कुल \(90^\circ\) है। परीक्षा में शब्दों को चरणों में बदलें।
\(\theta=150^\circ\), and \(150^\circ=\frac{5\pi}{6}\). In exams, first find the angle, then convert into radians.
Step 2
Why this answer is correct
The correct answer is C. \(\frac{5\pi}{6}\). \(\theta=150^\circ\), and \(150^\circ=\frac{5\pi}{6}\). In exams, first find the angle, then convert into radians.
Step 3
Exam Tip
\(\theta=150^\circ\) और \(150^\circ=\frac{5\pi}{6}\) होता है। परीक्षा में पहले कोण निकालें, फिर रेडियन में बदलें।
\(2\times\frac{180^\circ}{\pi}=2\times\frac{180^\circ\times7}{22}=114\frac{6}{11}^\circ\). In exams, use the given value of \(\pi\).
Step 2
Why this answer is correct
The correct answer is A. \(114\frac{6}{11}^\circ\). \(2\times\frac{180^\circ}{\pi}=2\times\frac{180^\circ\times7}{22}=114\frac{6}{11}^\circ\). In exams, use the given value of \(\pi\).
Step 3
Exam Tip
\(2\times\frac{180^\circ}{\pi}=2\times\frac{180^\circ\times7}{22}=114\frac{6}{11}^\circ\) है। परीक्षा में दिए गए \(\pi\) के मान का ही प्रयोग करें।
Since \(180^\circ=\pi\) radians, \(1^\circ=\frac{\pi}{180}\) radians. Remember this basic conversion for exams.
Step 2
Why this answer is correct
The correct answer is D. \(\frac{\pi}{180}\). Since \(180^\circ=\pi\) radians, \(1^\circ=\frac{\pi}{180}\) radians. Remember this basic conversion for exams.
Step 3
Exam Tip
क्योंकि \(180^\circ=\pi\) रेडियन, इसलिए \(1^\circ=\frac{\pi}{180}\) रेडियन है। परीक्षा में इस मूल रूपांतरण को याद रखें।
Coterminal angles must differ by an integral multiple of \(2\pi\). The difference for \(-\frac{7\pi}{4}\) does not satisfy this.
Step 2
Why this answer is correct
The correct answer is B. \(-\frac{7\pi}{4}\). Coterminal angles must differ by an integral multiple of \(2\pi\). The difference for \(-\frac{7\pi}{4}\) does not satisfy this.
Step 3
Exam Tip
सह-टर्मिनल कोणों का अंतर \(2\pi\) का पूर्णांक गुणज होना चाहिए। \(-\frac{7\pi}{4}\) का अंतर ऐसा नहीं है।
\(135^\circ=\frac{3\pi}{4}\) and \(s=8\times\frac{3\pi}{4}=6\pi\). In exams, first convert degrees into radians.
Step 2
Why this answer is correct
The correct answer is C. \(6\pi\) सेमी / \(6\pi\) cm. \(135^\circ=\frac{3\pi}{4}\) and \(s=8\times\frac{3\pi}{4}=6\pi\). In exams, first convert degrees into radians.
Step 3
Exam Tip
\(135^\circ=\frac{3\pi}{4}\) और \(s=8\times\frac{3\pi}{4}=6\pi\) है। परीक्षा में डिग्री को पहले रेडियन में बदलें।
Adding \(2\pi\) five times to \(-\frac{29\pi}{6}\) gives \(\frac{\pi}{6}\). Always keep the principal angle in the given interval.
Step 2
Why this answer is correct
The correct answer is A. \(\frac{\pi}{6}\). Adding \(2\pi\) five times to \(-\frac{29\pi}{6}\) gives \(\frac{\pi}{6}\). Always keep the principal angle in the given interval.
Step 3
Exam Tip
\(-\frac{29\pi}{6}\) में (5) बार \(2\pi\) जोड़ने पर \(\frac{\pi}{6}\) मिलता है। प्रधान कोण हमेशा दी गई सीमा में रखें।
The coterminal angle of \(1234^\circ\) is \(154^\circ\), which lies in the second quadrant. In exams, first find the remainder after division by \(360^\circ\).
Step 2
Why this answer is correct
The correct answer is B. दूसरा चतुर्थांश / Second quadrant. The coterminal angle of \(1234^\circ\) is \(154^\circ\), which lies in the second quadrant. In exams, first find the remainder after division by \(360^\circ\).
Step 3
Exam Tip
\(1234^\circ\) का सह-टर्मिनल कोण \(154^\circ\) है, जो दूसरे चतुर्थांश में है। परीक्षा में पहले \(360^\circ\) से भाग देकर शेष देखें।
Multiplying \(-\frac{17\pi}{18}\) by \(180^\circ/\pi\) gives \(-170^\circ\). The negative sign shows direction.
Step 2
Why this answer is correct
The correct answer is C. \(-170^\circ\). Multiplying \(-\frac{17\pi}{18}\) by \(180^\circ/\pi\) gives \(-170^\circ\). The negative sign shows direction.
Step 3
Exam Tip
\(-\frac{17\pi}{18}\) को \(180^\circ/\pi\) से गुणा करने पर \(-170^\circ\) मिलता है। ऋण चिह्न दिशा बताता है।
One complete revolution is \(2\pi\) radians, so the measure is \(\frac{11}{6}\times2\pi=\frac{11\pi}{3}\). In exams, take a full turn as \(2\pi\).
Step 2
Why this answer is correct
The correct answer is A. \(\frac{11\pi}{3}\). One complete revolution is \(2\pi\) radians, so the measure is \(\frac{11}{6}\times2\pi=\frac{11\pi}{3}\). In exams, take a full turn as \(2\pi\).
Step 3
Exam Tip
एक पूर्ण चक्कर \(2\pi\) रेडियन होता है, इसलिए माप \(\frac{11}{6}\times2\pi=\frac{11\pi}{3}\) है। परीक्षा में पूर्ण चक्कर को \(2\pi\) मानें।
