Adding \(6\pi\) to \(-\frac{31\pi}{6}\) gives \(\frac{5\pi}{6}\). In exams, add multiples of \(2\pi\) to negative angles.
Step 2
Why this answer is correct
The correct answer is B. \(\frac{5\pi}{6}\). Adding \(6\pi\) to \(-\frac{31\pi}{6}\) gives \(\frac{5\pi}{6}\). In exams, add multiples of \(2\pi\) to negative angles.
Step 3
Exam Tip
\(-\frac{31\pi}{6}\) में \(6\pi\) जोड़ने पर \(\frac{5\pi}{6}\) मिलता है। परीक्षा में ऋणात्मक कोण में \(2\pi\) के गुणज जोड़ें।
D. \(165^\circ\), दूसरा चतुर्थांश/\(165^\circ\), second quadrant
Step 1
Concept
\(1245^\circ-1080^\circ=165^\circ\), so the angle lies in the second quadrant. In exams, first subtract multiples of \(360^\circ\).
Step 2
Why this answer is correct
The correct answer is D. \(165^\circ\), दूसरा चतुर्थांश / \(165^\circ\), second quadrant. \(1245^\circ-1080^\circ=165^\circ\), so the angle lies in the second quadrant. In exams, first subtract multiples of \(360^\circ\).
Step 3
Exam Tip
\(1245^\circ-1080^\circ=165^\circ\), इसलिए कोण दूसरे चतुर्थांश में है। परीक्षा में पहले \(360^\circ\) के गुणज घटाएं।
\(18^\circ45'=\frac{75}{4}^\circ\) and the radian measure is \(\frac{75\pi}{720}=\frac{5\pi}{48}\). In exams, first convert minutes into degrees.
Step 2
Why this answer is correct
The correct answer is A. \(\frac{5\pi}{48}\). \(18^\circ45'=\frac{75}{4}^\circ\) and the radian measure is \(\frac{75\pi}{720}=\frac{5\pi}{48}\). In exams, first convert minutes into degrees.
Step 3
Exam Tip
\(18^\circ45'=\frac{75}{4}^\circ\) और रेडियन मान \(\frac{75\pi}{720}=\frac{5\pi}{48}\) है। परीक्षा में मिनट को पहले डिग्री में बदलें।
From \(s=r\theta\), \(\theta=\frac{3\pi}{8}\), which is \(67.5^\circ\). In exams, keep the angle in radians in the arc formula.
Step 2
Why this answer is correct
The correct answer is C. \(67.5^\circ\). From \(s=r\theta\), \(\theta=\frac{3\pi}{8}\), which is \(67.5^\circ\). In exams, keep the angle in radians in the arc formula.
Step 3
Exam Tip
\(s=r\theta\) से \(\theta=\frac{3\pi}{8}\), जो \(67.5^\circ\) है। परीक्षा में चाप सूत्र में कोण रेडियन में रखें।
\(75\pi=\frac{1}{2}\times100\times\theta\), so \(\theta=\frac{3\pi}{2}=270^\circ\). In exams, \(\theta\) is in radians in the area formula.
Step 2
Why this answer is correct
The correct answer is D. \(270^\circ\). \(75\pi=\frac{1}{2}\times100\times\theta\), so \(\theta=\frac{3\pi}{2}=270^\circ\). In exams, \(\theta\) is in radians in the area formula.
Step 3
Exam Tip
\(75\pi=\frac{1}{2}\times100\times\theta\), इसलिए \(\theta=\frac{3\pi}{2}=270^\circ\)। परीक्षा में क्षेत्रफल सूत्र में \(\theta\) रेडियन में होता है।
\(-1540^\circ+1800^\circ=260^\circ\), so the principal coterminal angle is \(260^\circ\). In exams, add multiples of \(360^\circ\) to negative angles.
Step 2
Why this answer is correct
The correct answer is A. \(260^\circ\). \(-1540^\circ+1800^\circ=260^\circ\), so the principal coterminal angle is \(260^\circ\). In exams, add multiples of \(360^\circ\) to negative angles.
Step 3
Exam Tip
\(-1540^\circ+1800^\circ=260^\circ\), इसलिए मुख्य सह-प्रारंभिक कोण \(260^\circ\) है। परीक्षा में ऋणात्मक कोण में \(360^\circ\) के गुणज जोड़ें।
(7) revolutions are \(14\pi\) and \(135^\circ=\frac{3\pi}{4}\), so the total is \(\frac{59\pi}{4}\). In exams, convert revolutions and extra angle separately.
Step 2
Why this answer is correct
The correct answer is C. \(\frac{59\pi}{4}\). (7) revolutions are \(14\pi\) and \(135^\circ=\frac{3\pi}{4}\), so the total is \(\frac{59\pi}{4}\). In exams, convert revolutions and extra angle separately.
Step 3
Exam Tip
(7) चक्कर \(14\pi\) हैं और \(135^\circ=\frac{3\pi}{4}\), इसलिए कुल \(\frac{59\pi}{4}\) है। परीक्षा में चक्कर और अतिरिक्त कोण अलग-अलग बदलें।
The minute hand rotates \(2\pi\) in (60) minutes, so in (29) minutes it rotates \(\frac{29\pi}{30}\). In exams, use the time ratio.
Step 2
Why this answer is correct
The correct answer is B. \(\frac{29\pi}{30}\). The minute hand rotates \(2\pi\) in (60) minutes, so in (29) minutes it rotates \(\frac{29\pi}{30}\). In exams, use the time ratio.
Step 3
Exam Tip
मिनट सुई (60) मिनट में \(2\pi\) घूमती है, इसलिए (29) मिनट में \(\frac{29\pi}{30}\) घूमेगी। परीक्षा में समय का अनुपात लगाएं।
(5) hours (36) minutes \(=\frac{28}{5}\) hours and the hour hand rate is \(\frac{\pi}{6}\) radians per hour. Hence the angle is \(\frac{28}{5}\times\frac{\pi}{6}=\frac{14\pi}{15}\).
Step 2
Why this answer is correct
The correct answer is D. \(\frac{14\pi}{15}\). (5) hours (36) minutes \(=\frac{28}{5}\) hours and the hour hand rate is \(\frac{\pi}{6}\) radians per hour. Hence the angle is \(\frac{28}{5}\times\frac{\pi}{6}=\frac{14\pi}{15}\).
Step 3
Exam Tip
(5) घंटे (36) मिनट \(=\frac{28}{5}\) घंटे और घंटे सुई की दर \(\frac{\pi}{6}\) रेडियन प्रति घंटा है। इसलिए कोण \(\frac{28}{5}\times\frac{\pi}{6}=\frac{14\pi}{15}\) है।
The principal angle of \(\frac{41\pi}{7}\) is \(\frac{13\pi}{7}\), which lies in the fourth quadrant. The reference angle is \(2\pi-\frac{13\pi}{7}=\frac{\pi}{7}\).
Step 2
Why this answer is correct
The correct answer is A. \(\frac{\pi}{7}\). The principal angle of \(\frac{41\pi}{7}\) is \(\frac{13\pi}{7}\), which lies in the fourth quadrant. The reference angle is \(2\pi-\frac{13\pi}{7}=\frac{\pi}{7}\).
Step 3
Exam Tip
\(\frac{41\pi}{7}\) का मुख्य कोण \(\frac{13\pi}{7}\) है और वह चौथे चतुर्थांश में है। संदर्भ कोण \(2\pi-\frac{13\pi}{7}=\frac{\pi}{7}\) है।
In the second quadrant, the principal angle is \(\pi-\alpha\). Hence \(\pi-\frac{5\pi}{18}=\frac{13\pi}{18}\).
Step 2
Why this answer is correct
The correct answer is C. \(\frac{13\pi}{18}\). In the second quadrant, the principal angle is \(\pi-\alpha\). Hence \(\pi-\frac{5\pi}{18}=\frac{13\pi}{18}\).
Step 3
Exam Tip
दूसरे चतुर्थांश में मुख्य कोण \(\pi-\alpha\) होता है। इसलिए \(\pi-\frac{5\pi}{18}=\frac{13\pi}{18}\) है।
The principal angle of \(-\theta\) is \(110^\circ\), so the principal angle of \(\theta\) is \(-110^\circ+360^\circ=250^\circ\). In exams, adjust with \(360^\circ\) after changing the sign.
Step 2
Why this answer is correct
The correct answer is D. \(250^\circ\). The principal angle of \(-\theta\) is \(110^\circ\), so the principal angle of \(\theta\) is \(-110^\circ+360^\circ=250^\circ\). In exams, adjust with \(360^\circ\) after changing the sign.
Step 3
Exam Tip
\(-\theta\) का मुख्य कोण \(110^\circ\) है, इसलिए \(\theta\) का मुख्य कोण \(-110^\circ+360^\circ=250^\circ\) होगा। परीक्षा में संकेत बदलने पर \(360^\circ\) से समायोजन करें।
One complete revolution is \(360^\circ\) and \(\frac{1440^\circ}{360^\circ}=4\). In exams, divide the difference by \(360^\circ\).
Step 2
Why this answer is correct
The correct answer is B. (4). One complete revolution is \(360^\circ\) and \(\frac{1440^\circ}{360^\circ}=4\). In exams, divide the difference by \(360^\circ\).
Step 3
Exam Tip
एक पूर्ण चक्कर \(360^\circ\) होता है और \(\frac{1440^\circ}{360^\circ}=4\)। परीक्षा में अंतर को \(360^\circ\) से भाग दें।
\(20'=\frac{1}{3}^\circ\) and \(24''=\frac{1}{150}^\circ\), so the total is \(73.34^\circ\). In exams, convert minutes and seconds separately into degrees.
Step 2
Why this answer is correct
The correct answer is A. \(73.34^\circ\). \(20'=\frac{1}{3}^\circ\) and \(24''=\frac{1}{150}^\circ\), so the total is \(73.34^\circ\). In exams, convert minutes and seconds separately into degrees.
Step 3
Exam Tip
\(20'=\frac{1}{3}^\circ\) और \(24''=\frac{1}{150}^\circ\), इसलिए कुल \(73.34^\circ\) है। परीक्षा में मिनट और सेकंड को अलग-अलग डिग्री में बदलें।
Subtracting \(8\pi\) from \(\frac{107\pi}{12}\) gives \(\frac{11\pi}{12}\). \(\frac{11\pi}{12}\) lies in the second quadrant.
Step 2
Why this answer is correct
The correct answer is C. दूसरा चतुर्थांश / Second quadrant. Subtracting \(8\pi\) from \(\frac{107\pi}{12}\) gives \(\frac{11\pi}{12}\). \(\frac{11\pi}{12}\) lies in the second quadrant.
Step 3
Exam Tip
\(\frac{107\pi}{12}\) में से \(8\pi\) घटाने पर \(\frac{11\pi}{12}\) मिलता है। \(\frac{11\pi}{12}\) दूसरा चतुर्थांश में है।
The smaller counterclockwise angle is \(2\pi-\frac{11\pi}{6}=\frac{\pi}{6}\). In exams, subtract the larger part from one full rotation.
Step 2
Why this answer is correct
The correct answer is D. \(\frac{\pi}{6}\). The smaller counterclockwise angle is \(2\pi-\frac{11\pi}{6}=\frac{\pi}{6}\). In exams, subtract the larger part from one full rotation.
Step 3
Exam Tip
छोटा प्रतिघड़ी कोण \(2\pi-\frac{11\pi}{6}=\frac{\pi}{6}\) है। परीक्षा में एक पूर्ण चक्कर से बड़ा भाग घटाएं।
From \(s=r\theta\), (r=4), then \(A=\frac{1}{2}r^2\theta=32\). In exams, first find the radius and then apply the area formula.
Step 2
Why this answer is correct
The correct answer is A. (32) वर्ग सेमी / (32) square cm. From \(s=r\theta\), (r=4), then \(A=\frac{1}{2}r^2\theta=32\). In exams, first find the radius and then apply the area formula.
Step 3
Exam Tip
\(s=r\theta\) से (r=4), फिर \(A=\frac{1}{2}r^2\theta=32\)। परीक्षा में पहले त्रिज्या निकालकर क्षेत्रफल लगाएं।
\(126^\circ=\frac{126\pi}{180}=\frac{7\pi}{10}=\frac{14\pi}{20}\), so (m=14). In exams, make the denominator match the given form.
Step 2
Why this answer is correct
The correct answer is C. (14). \(126^\circ=\frac{126\pi}{180}=\frac{7\pi}{10}=\frac{14\pi}{20}\), so (m=14). In exams, make the denominator match the given form.
Step 3
Exam Tip
\(126^\circ=\frac{126\pi}{180}=\frac{7\pi}{10}=\frac{14\pi}{20}\), इसलिए (m=14)। परीक्षा में दिए रूप जैसा हर बनाएं।
\(300^\circ=\frac{5\pi}{3}=\frac{15\pi}{9}\), so (p=15). In exams, convert degrees to radians and then match denominators.
Step 2
Why this answer is correct
The correct answer is D. (15). \(300^\circ=\frac{5\pi}{3}=\frac{15\pi}{9}\), so (p=15). In exams, convert degrees to radians and then match denominators.
Step 3
Exam Tip
\(300^\circ=\frac{5\pi}{3}=\frac{15\pi}{9}\), इसलिए (p=15)। परीक्षा में डिग्री से रेडियन बदलकर समान हर बनाएं।
\(-\frac{83\pi}{10}+10\pi=\frac{17\pi}{10}\). In exams, add a suitable large multiple of \(2\pi\) to bring the angle into the given interval.
Step 2
Why this answer is correct
The correct answer is B. \(\frac{17\pi}{10}\). \(-\frac{83\pi}{10}+10\pi=\frac{17\pi}{10}\). In exams, add a suitable large multiple of \(2\pi\) to bring the angle into the given interval.
Step 3
Exam Tip
\(-\frac{83\pi}{10}+10\pi=\frac{17\pi}{10}\)। परीक्षा में \(2\pi\) के बड़े गुणज जोड़कर कोण को दिए अंतराल में लाएं।
The wheel circumference is \(70\pi=220\) cm, so it makes (14) revolutions. The total angle is \(14\times2\pi=28\pi\) radians.
Step 2
Why this answer is correct
The correct answer is A. \(28\pi\). The wheel circumference is \(70\pi=220\) cm, so it makes (14) revolutions. The total angle is \(14\times2\pi=28\pi\) radians.
Step 3
Exam Tip
पहिए की परिधि \(70\pi=220\) सेमी है, इसलिए चक्कर (14) होंगे। कुल कोण \(14\times2\pi=28\pi\) रेडियन है।
\(144^\circ=\frac{4\pi}{5}\) and \(A=\frac{1}{2}\times225\times\frac{4\pi}{5}=90\pi\). In exams, converting degrees into radians is essential.
Step 2
Why this answer is correct
The correct answer is C. \(90\pi\) वर्ग सेमी / \(90\pi\) square cm. \(144^\circ=\frac{4\pi}{5}\) and \(A=\frac{1}{2}\times225\times\frac{4\pi}{5}=90\pi\). In exams, converting degrees into radians is essential.
Step 3
Exam Tip
\(144^\circ=\frac{4\pi}{5}\) और \(A=\frac{1}{2}\times225\times\frac{4\pi}{5}=90\pi\)। परीक्षा में डिग्री को रेडियन में बदलना जरूरी है।
The original angle is \(\pi-\frac{7\pi}{15}=\frac{8\pi}{15}\), which equals \(96^\circ\). In exams, keep the sum of supplementary angles as \(180^\circ\).
Step 2
Why this answer is correct
The correct answer is D. \(96^\circ\). The original angle is \(\pi-\frac{7\pi}{15}=\frac{8\pi}{15}\), which equals \(96^\circ\). In exams, keep the sum of supplementary angles as \(180^\circ\).
Step 3
Exam Tip
मूल कोण \(\pi-\frac{7\pi}{15}=\frac{8\pi}{15}\) है, जो \(96^\circ\) के बराबर है। परीक्षा में संपूरक कोणों का योग \(180^\circ\) रखें।
The complementary angle is \(90^\circ-37^\circ48'=52^\circ12'\). In exams, remember \(1^\circ=60'\) while borrowing.
Step 2
Why this answer is correct
The correct answer is B. \(52^\circ12'\). The complementary angle is \(90^\circ-37^\circ48'=52^\circ12'\). In exams, remember \(1^\circ=60'\) while borrowing.
Step 3
Exam Tip
पूरक कोण \(90^\circ-37^\circ48'=52^\circ12'\) है। परीक्षा में उधार लेते समय \(1^\circ=60'\) याद रखें।
Since \(\frac{\pi}{2}<\frac{9}{5}<\pi\), the angle lies in the second quadrant. In exams, compare with \(\frac{\pi}{2}\approx1.57\) and \(\pi\approx3.14\).
Step 2
Why this answer is correct
The correct answer is C. दूसरा चतुर्थांश / Second quadrant. Since \(\frac{\pi}{2}<\frac{9}{5}<\pi\), the angle lies in the second quadrant. In exams, compare with \(\frac{\pi}{2}\approx1.57\) and \(\pi\approx3.14\).
Step 3
Exam Tip
\(\frac{\pi}{2}<\frac{9}{5}<\pi\), इसलिए कोण दूसरे चतुर्थांश में है। परीक्षा में \(\frac{\pi}{2}\approx1.57\) और \(\pi\approx3.14\) से तुलना करें।
From \(A=\frac{1}{2}rs\), (r=8), then \(\theta=\frac{s}{r}=\frac{25}{8}\). In exams, find the radius first from arc length and area.
Step 2
Why this answer is correct
The correct answer is B. \(\frac{25}{8}\). From \(A=\frac{1}{2}rs\), (r=8), then \(\theta=\frac{s}{r}=\frac{25}{8}\). In exams, find the radius first from arc length and area.
Step 3
Exam Tip
\(A=\frac{1}{2}rs\) से (r=8), फिर \(\theta=\frac{s}{r}=\frac{25}{8}\)। परीक्षा में चाप और क्षेत्रफल से पहले त्रिज्या निकालें।
\(15^\circ\) per second gives \(900^\circ\) per minute, and \(900^\circ=5\pi\) radians. In exams, convert the time unit first.
Step 2
Why this answer is correct
The correct answer is C. \(5\pi\). \(15^\circ\) per second gives \(900^\circ\) per minute, and \(900^\circ=5\pi\) radians. In exams, convert the time unit first.
Step 3
Exam Tip
\(15^\circ\) प्रति सेकंड से \(900^\circ\) प्रति मिनट मिलता है, और \(900^\circ=5\pi\) रेडियन है। परीक्षा में समय इकाई पहले बदलें।
The angle is \(\frac{3\pi}{8}\times10=\frac{15\pi}{4}\) radians, which is \(675^\circ\). In exams, first find the total radians.
Step 2
Why this answer is correct
The correct answer is A. \(675^\circ\). The angle is \(\frac{3\pi}{8}\times10=\frac{15\pi}{4}\) radians, which is \(675^\circ\). In exams, first find the total radians.
Step 3
Exam Tip
कोण \(\frac{3\pi}{8}\times10=\frac{15\pi}{4}\) रेडियन है, जो \(675^\circ\) है। परीक्षा में पहले कुल रेडियन निकालें।
\(81^\circ=\frac{9\pi}{20}\), so \(\frac{3x\pi}{20}=\frac{9\pi}{20}\) gives (x=3). In exams, write both angles in the same unit.
Step 2
Why this answer is correct
The correct answer is B. (3). \(81^\circ=\frac{9\pi}{20}\), so \(\frac{3x\pi}{20}=\frac{9\pi}{20}\) gives (x=3). In exams, write both angles in the same unit.
Step 3
Exam Tip
\(81^\circ=\frac{9\pi}{20}\), इसलिए \(\frac{3x\pi}{20}=\frac{9\pi}{20}\) से (x=3)। परीक्षा में दोनों कोणों को समान इकाई में लिखें।
\(-420^\circ30'+720^\circ=299^\circ30'\). In exams, add multiples of \(360^\circ\) even for mixed degree-minute angles.
Step 2
Why this answer is correct
The correct answer is C. \(299^\circ30'\). \(-420^\circ30'+720^\circ=299^\circ30'\). In exams, add multiples of \(360^\circ\) even for mixed degree-minute angles.
Step 3
Exam Tip
\(-420^\circ30'+720^\circ=299^\circ30'\)। परीक्षा में मिश्रित डिग्री-मिनट कोण पर भी \(360^\circ\) के गुणज जोड़ें।
\(\frac{58\pi}{9}-6\pi=\frac{4\pi}{9}\). In exams, subtract multiples of \(2\pi\) to keep the angle in the interval.
Step 2
Why this answer is correct
The correct answer is A. \(\frac{4\pi}{9}\). \(\frac{58\pi}{9}-6\pi=\frac{4\pi}{9}\). In exams, subtract multiples of \(2\pi\) to keep the angle in the interval.
Step 3
Exam Tip
\(\frac{58\pi}{9}-6\pi=\frac{4\pi}{9}\)। परीक्षा में \(2\pi\) के गुणज घटाकर अंतराल में कोण रखें।
The difference between the two angles is \(4\pi\), which is a multiple of \(2\pi\). Therefore, they are coterminal.
Step 2
Why this answer is correct
The correct answer is D. वे सह-प्रारंभिक हैं / They are coterminal. The difference between the two angles is \(4\pi\), which is a multiple of \(2\pi\). Therefore, they are coterminal.
Step 3
Exam Tip
दोनों कोणों का अंतर \(4\pi\) है, जो \(2\pi\) का गुणज है। इसलिए वे सह-प्रारंभिक हैं।
The principal angle in the fourth quadrant is \(333^\circ\), and its greatest negative coterminal angle is \(333^\circ-360^\circ=-27^\circ\). In exams, keep the greatest negative angle above \(-360^\circ\).
Step 2
Why this answer is correct
The correct answer is B. \(-27^\circ\). The principal angle in the fourth quadrant is \(333^\circ\), and its greatest negative coterminal angle is \(333^\circ-360^\circ=-27^\circ\). In exams, keep the greatest negative angle above \(-360^\circ\).
Step 3
Exam Tip
चौथे चतुर्थांश का मुख्य कोण \(333^\circ\) है और उसका सबसे बड़ा ऋणात्मक सह-प्रारंभिक कोण \(333^\circ-360^\circ=-27^\circ\) है। परीक्षा में सबसे बड़ा ऋणात्मक कोण \(-360^\circ\) से ऊपर रखें।
\(36+18\theta=48\), so \(\theta=\frac{2}{3}\) radians. In degrees, this is \(\frac{2}{3}\times\frac{180}{\pi}=\frac{120}{\pi}^\circ\).
Step 2
Why this answer is correct
The correct answer is C. \(\frac{120}{\pi}^\circ\). \(36+18\theta=48\), so \(\theta=\frac{2}{3}\) radians. In degrees, this is \(\frac{2}{3}\times\frac{180}{\pi}=\frac{120}{\pi}^\circ\).
Step 3
Exam Tip
\(36+18\theta=48\), इसलिए \(\theta=\frac{2}{3}\) रेडियन है। डिग्री में यह \(\frac{2}{3}\times\frac{180}{\pi}=\frac{120}{\pi}^\circ\) है।
\(218^\circ24'=218.4^\circ=\frac{1092}{5}^\circ\), so the radian measure is \(\frac{91\pi}{75}\). In exams, convert (24') into \(0.4^\circ\).
Step 2
Why this answer is correct
The correct answer is A. \(\frac{91\pi}{75}\). \(218^\circ24'=218.4^\circ=\frac{1092}{5}^\circ\), so the radian measure is \(\frac{91\pi}{75}\). In exams, convert (24') into \(0.4^\circ\).
Step 3
Exam Tip
\(218^\circ24'=218.4^\circ=\frac{1092}{5}^\circ\), इसलिए रेडियन \(\frac{91\pi}{75}\) है। परीक्षा में (24') को \(0.4^\circ\) में बदलें।
\(54^\circ=\frac{3\pi}{10}\) and from \(s=r\theta\), \(r=\frac{9\pi}{\frac{3\pi}{10}}=30\). In exams, convert degrees into radians before using the arc formula.
Step 2
Why this answer is correct
The correct answer is D. (30) सेमी / (30) cm. \(54^\circ=\frac{3\pi}{10}\) and from \(s=r\theta\), \(r=\frac{9\pi}{\frac{3\pi}{10}}=30\). In exams, convert degrees into radians before using the arc formula.
Step 3
Exam Tip
\(54^\circ=\frac{3\pi}{10}\) और \(s=r\theta\) से \(r=\frac{9\pi}{\frac{3\pi}{10}}=30\)। परीक्षा में डिग्री को रेडियन में बदलकर ही चाप सूत्र लगाएं।
The complementary angle is \(\frac{\pi}{2}-\frac{2\pi}{7}=\frac{3\pi}{14}\). In degrees, it is \(\frac{270}{7}^\circ\).
Step 2
Why this answer is correct
The correct answer is C. \(\frac{270}{7}^\circ\). The complementary angle is \(\frac{\pi}{2}-\frac{2\pi}{7}=\frac{3\pi}{14}\). In degrees, it is \(\frac{270}{7}^\circ\).
Step 3
Exam Tip
पूरक कोण \(\frac{\pi}{2}-\frac{2\pi}{7}=\frac{3\pi}{14}\) है। डिग्री में यह \(\frac{270}{7}^\circ\) होगा।
\(-\frac{101\pi}{18}+6\pi=\frac{7\pi}{18}\). In exams, writing \(6\pi\) as \(\frac{108\pi}{18}\) makes addition easy.
Step 2
Why this answer is correct
The correct answer is A. \(\frac{7\pi}{18}\). \(-\frac{101\pi}{18}+6\pi=\frac{7\pi}{18}\). In exams, writing \(6\pi\) as \(\frac{108\pi}{18}\) makes addition easy.
Step 3
Exam Tip
\(-\frac{101\pi}{18}+6\pi=\frac{7\pi}{18}\)। परीक्षा में \(6\pi\) को \(\frac{108\pi}{18}\) लिखकर जोड़ना आसान होता है।
\(210^\circ=\frac{7\pi}{6}\), while \(\frac{5\pi}{6}=150^\circ\). In exams, convert all options into the same unit before comparing.
Step 2
Why this answer is correct
The correct answer is D. \(\frac{5\pi}{6}\). \(210^\circ=\frac{7\pi}{6}\), while \(\frac{5\pi}{6}=150^\circ\). In exams, convert all options into the same unit before comparing.
Step 3
Exam Tip
\(210^\circ=\frac{7\pi}{6}\), जबकि \(\frac{5\pi}{6}=150^\circ\) है। परीक्षा में सभी विकल्पों को एक ही इकाई में बदलकर तुलना करें।
\(\theta=1.65\pi\), which lies between \(\frac{3\pi}{2}\) and \(2\pi\). Therefore, the angle is in the fourth quadrant.
Step 2
Why this answer is correct
The correct answer is A. चौथा चतुर्थांश / Fourth quadrant. \(\theta=1.65\pi\), which lies between \(\frac{3\pi}{2}\) and \(2\pi\). Therefore, the angle is in the fourth quadrant.
Step 3
Exam Tip
\(\theta=1.65\pi\), जो \(\frac{3\pi}{2}\) और \(2\pi\) के बीच है। इसलिए कोण चौथे चतुर्थांश में है।
The rotation is \(-\frac{11}{8}\times2\pi=-\frac{11\pi}{4}\), and adding \(4\pi\) gives \(\frac{5\pi}{4}\). In exams, first convert revolutions into radians.
Step 2
Why this answer is correct
The correct answer is B. \(\frac{5\pi}{4}\). The rotation is \(-\frac{11}{8}\times2\pi=-\frac{11\pi}{4}\), and adding \(4\pi\) gives \(\frac{5\pi}{4}\). In exams, first convert revolutions into radians.
Step 3
Exam Tip
घूर्णन \(-\frac{11}{8}\times2\pi=-\frac{11\pi}{4}\) है और \(4\pi\) जोड़ने पर \(\frac{5\pi}{4}\) मिलता है। परीक्षा में चक्कर को पहले रेडियन में बदलें।
The angle is \(72^\circ-5\times360^\circ=-1728^\circ\). In exams, going behind means subtracting multiples of \(360^\circ\).
Step 2
Why this answer is correct
The correct answer is D. \(-1728^\circ\). The angle is \(72^\circ-5\times360^\circ=-1728^\circ\). In exams, going behind means subtracting multiples of \(360^\circ\).
Step 3
Exam Tip
कोण \(72^\circ-5\times360^\circ=-1728^\circ\) है। परीक्षा में पीछे जाने का अर्थ \(360^\circ\) के गुणज घटाना है।
A straight angle is \(\pi\) radians, so the remaining angle is \(\pi-3\) radians. In degrees, it is (\frac{180\(\pi-3\)}{\pi}).
Step 2
Why this answer is correct
The correct answer is A. (\frac{180\(\pi-3\)}{\pi}). A straight angle is \(\pi\) radians, so the remaining angle is \(\pi-3\) radians. In degrees, it is (\frac{180\(\pi-3\)}{\pi}).
Step 3
Exam Tip
सीधा कोण \(\pi\) रेडियन होता है, इसलिए शेष कोण \(\pi-3\) रेडियन है। डिग्री में यह (\frac{180\(\pi-3\)}{\pi}) होगा।
From \(s=r\theta\), \(\theta=\frac{\frac{5\pi r}{6}}{r}=\frac{5\pi}{6}\), which is \(150^\circ\). In exams, cancel (r) to find the angle.
Step 2
Why this answer is correct
The correct answer is C. \(150^\circ\). From \(s=r\theta\), \(\theta=\frac{\frac{5\pi r}{6}}{r}=\frac{5\pi}{6}\), which is \(150^\circ\). In exams, cancel (r) to find the angle.
Step 3
Exam Tip
\(s=r\theta\) से \(\theta=\frac{\frac{5\pi r}{6}}{r}=\frac{5\pi}{6}\), जो \(150^\circ\) है। परीक्षा में (r) को काटकर कोण निकालें।
