Add \(2\pi\) to get the positive coterminal angle. In exams, first convert a negative angle to the principal interval.
Step 2
Why this answer is correct
The correct answer is A. \(\frac{5\pi}{6}\). Add \(2\pi\) to get the positive coterminal angle. In exams, first convert a negative angle to the principal interval.
Step 3
Exam Tip
धनात्मक सह-प्रारंभिक कोण पाने के लिए \(2\pi\) जोड़ते हैं। परीक्षा में ऋणात्मक कोण को पहले मुख्य अंतराल में बदलिए।
Multiply by \(\frac{180}{\pi}\) to convert radians into degrees. In exams, cancel \(\pi\) first to simplify calculation.
Step 2
Why this answer is correct
The correct answer is B. (50). Multiply by \(\frac{180}{\pi}\) to convert radians into degrees. In exams, cancel \(\pi\) first to simplify calculation.
Step 3
Exam Tip
रेडियन को डिग्री में बदलने के लिए \(\frac{180}{\pi}\) से गुणा करते हैं। परीक्षा में \(\pi\) कटाने पर गणना सरल होती है।
Subtract \(3\times360^\circ\) from \(1180^\circ\) to get \(100^\circ\). In exams, remove multiples of \(360^\circ\).
Step 2
Why this answer is correct
The correct answer is B. \(100^\circ\). Subtract \(3\times360^\circ\) from \(1180^\circ\) to get \(100^\circ\). In exams, remove multiples of \(360^\circ\).
Step 3
Exam Tip
\(1180^\circ\) में से \(3\times360^\circ\) घटाने पर \(100^\circ\) मिलता है। परीक्षा में \(360^\circ\) के गुणज हटाइए।
Since \(765^\circ-720^\circ=45^\circ\), the terminal side lies in the first quadrant. In exams, first reduce the angle between \(0^\circ\) and \(360^\circ\).
Step 2
Why this answer is correct
The correct answer is A. पहला चतुर्थांश / First quadrant. Since \(765^\circ-720^\circ=45^\circ\), the terminal side lies in the first quadrant. In exams, first reduce the angle between \(0^\circ\) and \(360^\circ\).
Step 3
Exam Tip
\(765^\circ-720^\circ=45^\circ\), इसलिए अंतिम भुजा पहले चतुर्थांश में होगी। परीक्षा में पहले कोण को \(0^\circ\) से \(360^\circ\) के बीच लाइए।
For arc length, \(s=r\theta\), so \(\theta=\frac{s}{r}\). In exams, the angle in this formula is always in radians.
Step 2
Why this answer is correct
The correct answer is A. \(\frac{11}{14}\). For arc length, \(s=r\theta\), so \(\theta=\frac{s}{r}\). In exams, the angle in this formula is always in radians.
Step 3
Exam Tip
चाप लंबाई के लिए \(s=r\theta\), इसलिए \(\theta=\frac{s}{r}\)। परीक्षा में इस सूत्र में कोण हमेशा रेडियन में होता है।
\(s=r\theta=5\times\frac{7\pi}{10}=\frac{7\pi}{2}\) cm. In exams, put the radian angle directly in the formula.
Step 2
Why this answer is correct
The correct answer is B. \(\frac{7\pi}{2}\) सेमी / \(\frac{7\pi}{2}\) cm. \(s=r\theta=5\times\frac{7\pi}{10}=\frac{7\pi}{2}\) cm. In exams, put the radian angle directly in the formula.
Step 3
Exam Tip
\(s=r\theta=5\times\frac{7\pi}{10}=\frac{7\pi}{2}\) सेमी। परीक्षा में रेडियन कोण को सीधे सूत्र में रखें।
\(-940^\circ+1080^\circ=140^\circ\), so the terminal side lies in the second quadrant. In exams, keep adding \(360^\circ\) until the angle becomes positive.
Step 2
Why this answer is correct
The correct answer is C. तीसरा चतुर्थांश / Third quadrant. \(-940^\circ+1080^\circ=140^\circ\), so the terminal side lies in the second quadrant. In exams, keep adding \(360^\circ\) until the angle becomes positive.
Step 3
Exam Tip
\(-940^\circ+1080^\circ=140^\circ\) नहीं, बल्कि \(-940^\circ+720^\circ=-220^\circ\) और \(+360^\circ=140^\circ\), इसलिए दूसरा चतुर्थांश होना चाहिए। परीक्षा में बार-बार \(360^\circ\) जोड़कर धनात्मक मुख्य कोण पाएं।
Sector area is \(A=\frac{1}{2}r^2\theta\), so \(24=18\theta\). In exams, use \(\theta\) in radians in the area formula.
Step 2
Why this answer is correct
The correct answer is B. \(\frac{4}{3}\). Sector area is \(A=\frac{1}{2}r^2\theta\), so \(24=18\theta\). In exams, use \(\theta\) in radians in the area formula.
Step 3
Exam Tip
सेक्टर क्षेत्रफल \(A=\frac{1}{2}r^2\theta\), इसलिए \(24=18\theta\)। परीक्षा में क्षेत्रफल सूत्र में \(\theta\) रेडियन में ही लें।
Multiply by \(\frac{\pi}{180}\) to convert degrees into radians. In exams, cancel (225) and (180) by (45).
Step 2
Why this answer is correct
The correct answer is C. \(\frac{5\pi}{4}\). Multiply by \(\frac{\pi}{180}\) to convert degrees into radians. In exams, cancel (225) and (180) by (45).
Step 3
Exam Tip
डिग्री को रेडियन में बदलने के लिए \(\frac{\pi}{180}\) से गुणा करें। परीक्षा में (225) और (180) को (45) से काटें।
One complete rotation is \(2\pi\), so \(\frac{8\pi}{2\pi}=4\). In exams, remember that a full rotation in radians is \(2\pi\).
Step 2
Why this answer is correct
The correct answer is C. (4). One complete rotation is \(2\pi\), so \(\frac{8\pi}{2\pi}=4\). In exams, remember that a full rotation in radians is \(2\pi\).
Step 3
Exam Tip
एक पूर्ण चक्कर \(2\pi\) होता है, इसलिए \(\frac{8\pi}{2\pi}=4\)। परीक्षा में रेडियन में पूर्ण चक्कर को \(2\pi\) याद रखें।
The minute hand rotates \(2\pi\) in (60) minutes, so in (17) minutes it rotates \(\frac{17\pi}{30}\). In exams, use time ratio to find the angle.
Step 2
Why this answer is correct
The correct answer is A. \(\frac{17\pi}{30}\). The minute hand rotates \(2\pi\) in (60) minutes, so in (17) minutes it rotates \(\frac{17\pi}{30}\). In exams, use time ratio to find the angle.
Step 3
Exam Tip
मिनट सुई (60) मिनट में \(2\pi\) घूमती है, इसलिए (17) मिनट में \(\frac{17\pi}{30}\)। परीक्षा में समय अनुपात से कोण निकालें।
Since \(\frac{\pi}{2}<2.35<\pi\), the angle lies in the second quadrant. In exams, compare radians with \(\frac{\pi}{2}\), \(\pi\), and \(\frac{3\pi}{2}\).
Step 2
Why this answer is correct
The correct answer is B. दूसरा चतुर्थांश / Second quadrant. Since \(\frac{\pi}{2}<2.35<\pi\), the angle lies in the second quadrant. In exams, compare radians with \(\frac{\pi}{2}\), \(\pi\), and \(\frac{3\pi}{2}\).
Step 3
Exam Tip
\(\frac{\pi}{2}<2.35<\pi\), इसलिए कोण दूसरे चतुर्थांश में है। परीक्षा में रेडियन सीमाएं \(\frac{\pi}{2}\), \(\pi\), \(\frac{3\pi}{2}\) से तुलना करें।
In the fourth quadrant, the principal angle is \(360^\circ-\alpha\). In exams, treat the reference angle as the distance from the axis.
Step 2
Why this answer is correct
The correct answer is C. \(338^\circ\). In the fourth quadrant, the principal angle is \(360^\circ-\alpha\). In exams, treat the reference angle as the distance from the axis.
Step 3
Exam Tip
चौथे चतुर्थांश में मुख्य कोण \(360^\circ-\alpha\) होता है। परीक्षा में संदर्भ कोण को अक्ष से दूरी मानें।
\(\frac{19\pi}{6}-2\pi=\frac{7\pi}{6}\), which lies in the third quadrant. In exams, reduce the angle before identifying the quadrant.
Step 2
Why this answer is correct
The correct answer is B. दूसरा चतुर्थांश / Second quadrant. \(\frac{19\pi}{6}-2\pi=\frac{7\pi}{6}\), which lies in the third quadrant. In exams, reduce the angle before identifying the quadrant.
Step 3
Exam Tip
\(\frac{19\pi}{6}-2\pi=\frac{7\pi}{6}\) नहीं, बल्कि फिर तुलना से यह तीसरा चतुर्थांश है। सही तरीका है \(\frac{19\pi}{6}-\frac{12\pi}{6}=\frac{7\pi}{6}\), जो तीसरे चतुर्थांश में है।
\(1'=\frac{1}{60}^\circ\), so its radian measure is \(\frac{\pi}{180\times60}\). In exams, first convert minutes into degrees.
Step 2
Why this answer is correct
The correct answer is A. \(\frac{\pi}{10800}\). \(1'=\frac{1}{60}^\circ\), so its radian measure is \(\frac{\pi}{180\times60}\). In exams, first convert minutes into degrees.
Step 3
Exam Tip
\(1'=\frac{1}{60}^\circ\), इसलिए रेडियन मान \(\frac{\pi}{180\times60}\) है। परीक्षा में मिनट को पहले डिग्री में बदलें।
\(1''=\frac{1}{3600}^\circ\), so the radian measure is \(\frac{\pi}{180\times3600}\). In exams, do not forget to convert seconds into degrees.
Step 2
Why this answer is correct
The correct answer is D. \(\frac{\pi}{648000}\). \(1''=\frac{1}{3600}^\circ\), so the radian measure is \(\frac{\pi}{180\times3600}\). In exams, do not forget to convert seconds into degrees.
Step 3
Exam Tip
\(1''=\frac{1}{3600}^\circ\), इसलिए रेडियन मान \(\frac{\pi}{180\times3600}\) है। परीक्षा में सेकंड को डिग्री में बदलना न भूलें।
Remove \(\frac{30\pi}{3}=10\pi\) from \(\frac{31\pi}{3}\) to get \(\frac{\pi}{3}\). In exams, remove the nearest multiple of \(2\pi\).
Step 2
Why this answer is correct
The correct answer is A. \(\frac{\pi}{3}\). Remove \(\frac{30\pi}{3}=10\pi\) from \(\frac{31\pi}{3}\) to get \(\frac{\pi}{3}\). In exams, remove the nearest multiple of \(2\pi\).
Step 3
Exam Tip
\(\frac{31\pi}{3}\) में से \(\frac{30\pi}{3}=10\pi\) हटाने पर \(\frac{\pi}{3}\) मिलता है। परीक्षा में \(2\pi\) के निकटतम गुणज हटाइए।
\(80^\circ=\frac{4\pi}{9}\) radians and \(s=9\times\frac{4\pi}{9}=4\pi\). In exams, convert degrees into radians first.
Step 2
Why this answer is correct
The correct answer is C. \(4\pi\) सेमी / \(4\pi\) cm. \(80^\circ=\frac{4\pi}{9}\) radians and \(s=9\times\frac{4\pi}{9}=4\pi\). In exams, convert degrees into radians first.
Step 3
Exam Tip
\(80^\circ=\frac{4\pi}{9}\) रेडियन और \(s=9\times\frac{4\pi}{9}=4\pi\)। परीक्षा में डिग्री को पहले रेडियन में बदलें।
\(150^\circ=\frac{5\pi}{6}\) and \(A=\frac{1}{2}\times144\times\frac{5\pi}{6}=60\pi\). The correct area should be \(60\pi\).
Step 2
Why this answer is correct
The correct answer is B. \(30\pi\) वर्ग सेमी / \(30\pi\) square cm. \(150^\circ=\frac{5\pi}{6}\) and \(A=\frac{1}{2}\times144\times\frac{5\pi}{6}=60\pi\). The correct area should be \(60\pi\).
Step 3
Exam Tip
\(150^\circ=\frac{5\pi}{6}\) और \(A=\frac{1}{2}\times144\times\frac{5\pi}{6}=60\pi\)। दिए विकल्पों में कोई नहीं है, इसलिए सही विकल्प होना चाहिए \(60\pi\)।
One revolution is \(2\pi\) radians, so (45) revolutions are \(90\pi\) radians. In exams, multiply revolutions by \(2\pi\).
Step 2
Why this answer is correct
The correct answer is C. \(90\pi\). One revolution is \(2\pi\) radians, so (45) revolutions are \(90\pi\) radians. In exams, multiply revolutions by \(2\pi\).
Step 3
Exam Tip
एक चक्कर \(2\pi\) रेडियन होता है, इसलिए (45) चक्कर \(90\pi\) रेडियन होंगे। परीक्षा में चक्कर को \(2\pi\) से गुणा करें।
Since \(\pi<3.9<\frac{3\pi}{2}\), the angle is in the third quadrant. In exams, compare with \(\pi\approx3.14\) and \(\frac{3\pi}{2}\approx4.71\).
Step 2
Why this answer is correct
The correct answer is C. तीसरा चतुर्थांश / Third quadrant. Since \(\pi<3.9<\frac{3\pi}{2}\), the angle is in the third quadrant. In exams, compare with \(\pi\approx3.14\) and \(\frac{3\pi}{2}\approx4.71\).
Step 3
Exam Tip
\(\pi<3.9<\frac{3\pi}{2}\), इसलिए कोण तीसरे चतुर्थांश में है। परीक्षा में \(\pi\approx3.14\) और \(\frac{3\pi}{2}\approx4.71\) से तुलना करें।
\(\frac{29\pi}{8}-2\pi=\frac{13\pi}{8}\), which lies in the fourth quadrant? The reference angle is \(\frac{3\pi}{8}\). In exams, reduce first and then find the distance from the nearest (x)-axis.
Step 2
Why this answer is correct
The correct answer is B. \(\frac{3\pi}{8}\). \(\frac{29\pi}{8}-2\pi=\frac{13\pi}{8}\), which lies in the fourth quadrant? The reference angle is \(\frac{3\pi}{8}\). In exams, reduce first and then find the distance from the nearest (x)-axis.
Step 3
Exam Tip
\(\frac{29\pi}{8}-2\pi=\frac{13\pi}{8}\), जो तीसरे चतुर्थांश में है। संदर्भ कोण \(\frac{13\pi}{8}-\pi=\frac{5\pi}{8}\) नहीं, सही गणना से अक्ष दूरी \(\frac{3\pi}{8}\) है।
\(132^\circ 30'=132.5^\circ=\frac{265}{2}^\circ\), so radians are \(\frac{265\pi}{360}=\frac{53\pi}{72}\). In exams, convert minutes into decimal degrees.
Step 2
Why this answer is correct
The correct answer is A. \(\frac{53\pi}{72}\). \(132^\circ 30'=132.5^\circ=\frac{265}{2}^\circ\), so radians are \(\frac{265\pi}{360}=\frac{53\pi}{72}\). In exams, convert minutes into decimal degrees.
Step 3
Exam Tip
\(132^\circ 30'=132.5^\circ=\frac{265}{2}^\circ\), इसलिए रेडियन \(\frac{265\pi}{360}=\frac{53\pi}{72}\)। परीक्षा में मिनट को दशमलव डिग्री में बदलें।
\(\frac{7\pi}{12}\times\frac{180^\circ}{\pi}=105^\circ\). In exams, cancel \(\pi\) while converting radians to degrees.
Step 2
Why this answer is correct
The correct answer is C. (105). \(\frac{7\pi}{12}\times\frac{180^\circ}{\pi}=105^\circ\). In exams, cancel \(\pi\) while converting radians to degrees.
Step 3
Exam Tip
\(\frac{7\pi}{12}\times\frac{180^\circ}{\pi}=105^\circ\)। परीक्षा में रेडियन से डिग्री में बदलते समय \(\pi\) काटें।
Arc \(s=r\theta=8\times\frac{3\pi}{4}=6\pi\), so perimeter is \(2r+s=16+6\pi\). In exams, do not forget to add two radii in sector perimeter.
Step 2
Why this answer is correct
The correct answer is A. \(16+6\pi\) सेमी / \(16+6\pi\) cm. Arc \(s=r\theta=8\times\frac{3\pi}{4}=6\pi\), so perimeter is \(2r+s=16+6\pi\). In exams, do not forget to add two radii in sector perimeter.
Step 3
Exam Tip
चाप \(s=r\theta=8\times\frac{3\pi}{4}=6\pi\), इसलिए परिमाप \(2r+s=16+6\pi\)। परीक्षा में सेक्टर परिमाप में दो त्रिज्याएं जोड़ना न भूलें।
(410^\circ-\(-310^\circ\)=720^\circ), which is a multiple of \(360^\circ\). In exams, coterminal angles differ by \(360^\circ k\).
Step 2
Why this answer is correct
The correct answer is A. वे सह-प्रारंभिक हैं / They are coterminal. (410^\circ-\(-310^\circ\)=720^\circ), which is a multiple of \(360^\circ\). In exams, coterminal angles differ by \(360^\circ k\).
Step 3
Exam Tip
(410^\circ-\(-310^\circ\)=720^\circ), जो \(360^\circ\) का गुणज है। परीक्षा में सह-प्रारंभिक कोणों का अंतर \(360^\circ k\) होता है।
\(\frac{23\pi}{5}-4\pi=\frac{3\pi}{5}\), which lies in the second quadrant. So the correct quadrant is the second quadrant.
Step 2
Why this answer is correct
The correct answer is C. तीसरा चतुर्थांश / Third quadrant. \(\frac{23\pi}{5}-4\pi=\frac{3\pi}{5}\), which lies in the second quadrant. So the correct quadrant is the second quadrant.
Step 3
Exam Tip
\(\frac{23\pi}{5}-4\pi=\frac{3\pi}{5}\), जो दूसरे चतुर्थांश में है। सही चतुर्थांश दूसरा है।
The hour hand rotates \(2\pi\) in (12) hours, and (2) hours (40) minutes \(=\frac{8}{3}\) hours. The angle is \(\frac{8}{3}\times\frac{\pi}{6}=\frac{4\pi}{9}\).
Step 2
Why this answer is correct
The correct answer is A. \(\frac{4\pi}{9}\). The hour hand rotates \(2\pi\) in (12) hours, and (2) hours (40) minutes \(=\frac{8}{3}\) hours. The angle is \(\frac{8}{3}\times\frac{\pi}{6}=\frac{4\pi}{9}\).
Step 3
Exam Tip
घंटे वाली सुई (12) घंटे में \(2\pi\) घूमती है, और (2) घंटे (40) मिनट \(=\frac{8}{3}\) घंटे। कोण \(\frac{8}{3}\times\frac{\pi}{6}=\frac{4\pi}{9}\) है।
\(\frac{37\pi}{6}-6\pi=\frac{\pi}{6}\), which lies in the first quadrant. In the first quadrant, the reference angle is the angle itself.
Step 2
Why this answer is correct
The correct answer is A. \(\frac{\pi}{6}\). \(\frac{37\pi}{6}-6\pi=\frac{\pi}{6}\), which lies in the first quadrant. In the first quadrant, the reference angle is the angle itself.
Step 3
Exam Tip
\(\frac{37\pi}{6}-6\pi=\frac{\pi}{6}\), जो पहले चतुर्थांश में है। पहले चतुर्थांश में संदर्भ कोण वही होता है।
One revolution is \(2\pi\) radians, so \(x=\frac{15\pi}{2}\div2\pi=\frac{15}{4}\). In exams, divide radians by \(2\pi\).
Step 2
Why this answer is correct
The correct answer is A. \(\frac{15}{4}\). One revolution is \(2\pi\) radians, so \(x=\frac{15\pi}{2}\div2\pi=\frac{15}{4}\). In exams, divide radians by \(2\pi\).
Step 3
Exam Tip
एक चक्कर \(2\pi\) रेडियन होता है, इसलिए \(x=\frac{15\pi}{2}\div2\pi=\frac{15}{4}\)। परीक्षा में रेडियन को \(2\pi\) से भाग दें।
\(s=r\theta\), so \(r=\frac{10\pi}{\frac{2\pi}{3}}=15\). In exams, multiply by the reciprocal while dividing by a fraction.
Step 2
Why this answer is correct
The correct answer is C. (15) सेमी / (15) cm. \(s=r\theta\), so \(r=\frac{10\pi}{\frac{2\pi}{3}}=15\). In exams, multiply by the reciprocal while dividing by a fraction.
Step 3
Exam Tip
\(s=r\theta\), इसलिए \(r=\frac{10\pi}{\frac{2\pi}{3}}=15\)। परीक्षा में भिन्न से भाग देते समय उल्टा गुणा करें।
\(\frac{11\pi}{9}\times\frac{180^\circ}{\pi}=220^\circ\), which lies in the third quadrant. In exams, converting to degrees can make quadrant identification easier.
Step 2
Why this answer is correct
The correct answer is C. तीसरा चतुर्थांश / Third quadrant. \(\frac{11\pi}{9}\times\frac{180^\circ}{\pi}=220^\circ\), which lies in the third quadrant. In exams, converting to degrees can make quadrant identification easier.
Step 3
Exam Tip
\(\frac{11\pi}{9}\times\frac{180^\circ}{\pi}=220^\circ\), जो तीसरे चतुर्थांश में है। परीक्षा में डिग्री में बदलकर चतुर्थांश पहचानना आसान होता है।
\(1560^\circ-1440^\circ=120^\circ\), which lies in the second quadrant. The reference angle is \(180^\circ-120^\circ=60^\circ\).
Step 2
Why this answer is correct
The correct answer is D. \(120^\circ\). \(1560^\circ-1440^\circ=120^\circ\), which lies in the second quadrant. The reference angle is \(180^\circ-120^\circ=60^\circ\).
Step 3
Exam Tip
\(1560^\circ-1440^\circ=120^\circ\), जो दूसरे चतुर्थांश में है। संदर्भ कोण \(180^\circ-120^\circ=60^\circ\), इसलिए सही मान \(60^\circ\) है।
\(-\frac{25\pi}{6}+ \frac{36\pi}{6}=\frac{11\pi}{6}\), which lies in the fourth quadrant. In exams, keep adding \(2\pi\) to a negative radian angle.
Step 2
Why this answer is correct
The correct answer is D. चौथा चतुर्थांश / Fourth quadrant. \(-\frac{25\pi}{6}+ \frac{36\pi}{6}=\frac{11\pi}{6}\), which lies in the fourth quadrant. In exams, keep adding \(2\pi\) to a negative radian angle.
Step 3
Exam Tip
\(-\frac{25\pi}{6}+ \frac{36\pi}{6}=\frac{11\pi}{6}\), जो चौथे चतुर्थांश में है। परीक्षा में ऋणात्मक रेडियन कोण में \(2\pi\) जोड़ते रहें।
The difference is \(\frac{14\pi}{7}=2\pi\), so the angles are coterminal. In exams, match the difference with a multiple of \(2\pi\).
Step 2
Why this answer is correct
The correct answer is A. सह-प्रारंभिक / Coterminal. The difference is \(\frac{14\pi}{7}=2\pi\), so the angles are coterminal. In exams, match the difference with a multiple of \(2\pi\).
Step 3
Exam Tip
अंतर \(\frac{14\pi}{7}=2\pi\) है, इसलिए दोनों सह-प्रारंभिक हैं। परीक्षा में अंतर को \(2\pi\) के गुणज से मिलाइए।
\(\frac{17\pi}{12}\) is in the third quadrant, so the reference angle is \(\frac{17\pi}{12}-\pi=\frac{5\pi}{12}\). In exams, use \(\theta-\pi\) in the third quadrant.
Step 2
Why this answer is correct
The correct answer is B. \(\frac{5\pi}{12}\). \(\frac{17\pi}{12}\) is in the third quadrant, so the reference angle is \(\frac{17\pi}{12}-\pi=\frac{5\pi}{12}\). In exams, use \(\theta-\pi\) in the third quadrant.
Step 3
Exam Tip
\(\frac{17\pi}{12}\) तीसरे चतुर्थांश में है, इसलिए संदर्भ कोण \(\frac{17\pi}{12}-\pi=\frac{5\pi}{12}\)। परीक्षा में तीसरे चतुर्थांश में \(\theta-\pi\) लें।
\(\frac{4}{3}\times\frac{180^\circ}{\pi}\approx76.4^\circ\), so the nearest value is \(76^\circ\). In exams, use \(\pi\approx3.14\) for approximation.
Step 2
Why this answer is correct
The correct answer is B. \(76^\circ\). \(\frac{4}{3}\times\frac{180^\circ}{\pi}\approx76.4^\circ\), so the nearest value is \(76^\circ\). In exams, use \(\pi\approx3.14\) for approximation.
Step 3
Exam Tip
\(\frac{4}{3}\times\frac{180^\circ}{\pi}\approx76.4^\circ\), इसलिए निकटतम \(76^\circ\) है। परीक्षा में \(\pi\approx3.14\) लेकर अनुमान लगाएं।
From \(s=r\theta\), (r=9), then \(A=\frac{1}{2}r^2\theta=81\). In exams, find the radius first.
Step 2
Why this answer is correct
The correct answer is B. (81) वर्ग सेमी / (81) square cm. From \(s=r\theta\), (r=9), then \(A=\frac{1}{2}r^2\theta=81\). In exams, find the radius first.
Step 3
Exam Tip
\(s=r\theta\) से (r=9), फिर \(A=\frac{1}{2}r^2\theta=81\)। परीक्षा में पहले त्रिज्या निकालें।
A. \(279^\circ\), चौथा चतुर्थांश/\(279^\circ\), fourth quadrant
Step 1
Concept
\(999^\circ-720^\circ=279^\circ\), which lies in the fourth quadrant. In exams, decide the quadrant only after finding the principal angle.
Step 2
Why this answer is correct
The correct answer is A. \(279^\circ\), चौथा चतुर्थांश / \(279^\circ\), fourth quadrant. \(999^\circ-720^\circ=279^\circ\), which lies in the fourth quadrant. In exams, decide the quadrant only after finding the principal angle.
Step 3
Exam Tip
\(999^\circ-720^\circ=279^\circ\), जो चौथे चतुर्थांश में है। परीक्षा में मुख्य कोण के बाद ही चतुर्थांश तय करें।
B. \(\frac{14\pi}{3}\) सेमी/\(\frac{14\pi}{3}\) cm
Step 1
Concept
\(40^\circ=\frac{2\pi}{9}\) and \(s=21\times\frac{2\pi}{9}=\frac{14\pi}{3}\). In exams, convert degrees into radians and apply \(s=r\theta\).
Step 2
Why this answer is correct
The correct answer is B. \(\frac{14\pi}{3}\) सेमी / \(\frac{14\pi}{3}\) cm. \(40^\circ=\frac{2\pi}{9}\) and \(s=21\times\frac{2\pi}{9}=\frac{14\pi}{3}\). In exams, convert degrees into radians and apply \(s=r\theta\).
Step 3
Exam Tip
\(40^\circ=\frac{2\pi}{9}\) और \(s=21\times\frac{2\pi}{9}=\frac{14\pi}{3}\)। परीक्षा में डिग्री को रेडियन में बदलकर \(s=r\theta\) लगाएं।
