100 results found for "radians" in all classes.
Convert the angle \(23^\circ45'\) into radians.
B. \(\frac{19\pi}{144}\)
\(23^\circ45'=\frac{95}{4}^\circ\) होता है। रेडियन में \(\frac{95}{4}\times\frac{\pi}{180}=\frac{19\pi}{144}\) है। / \(23^\circ45'=\frac{95}{4}^\circ\). In radians it is \(\frac{95}{4}\times\frac{\pi}{180}=\frac{19\pi}{144}\).
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Convert \(165^\circ\) into radians.
C. \( \frac{11\pi}{12} \) रेडियन\( \frac{11\pi}{12} \) radians
\(165^\circ=\frac{165\pi}{180}=\frac{11\pi}{12}\) है। \(15^\circ\) के गुणजों में हर (12) आ सकता है। / \(165^\circ=\frac{165\pi}{180}=\frac{11\pi}{12}\). Multiples of \(15^\circ\) can lead to denominator (12).
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Convert \(90^\circ\) into radians.
D. \( \frac{\pi}{2} \) रेडियन\( \frac{\pi}{2} \) radians
\(90^\circ\) आधा \(180^\circ\) है इसलिए मान \( \frac{\pi}{2} \) है। पहले कोण को \(180^\circ\) से भाग दें। / \(90^\circ\) is half of \(180^\circ\) so it is \( \frac{\pi}{2} \). Divide the degree measure by \(180^\circ\) first.
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\(\frac{2\pi}{3}\) radians is equal to how many degrees?
A. \(120^\circ\)
\(\frac{2\pi}{3} \times \frac{180^\circ}{\pi}=120^\circ\) होता है। \(\pi\) हटाकर सरल गुणा करें। / \(\frac{2\pi}{3} \times \frac{180^\circ}{\pi}=120^\circ\). Cancel \(\pi\) and multiply simply.
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D. \(50^\circ\)
\(\frac{7\pi}{18}=70^\circ\), इसलिए मूल कोण \(70^\circ-20^\circ=50^\circ\) है। परीक्षा में अंतिम माप को पहले डिग्री में बदलें। / \(\frac{7\pi}{18}=70^\circ\), so the original angle is \(70^\circ-20^\circ=50^\circ\). In exams, first convert the final measure into degrees.
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If \(\frac{k\pi}{18}\) radians equals \(130^\circ\), what is the value of (k)?
C. (13)
\(130^\circ=\frac{13\pi}{18}\), इसलिए (k=13) है। परीक्षा में \(180^\circ=\pi\) से तुलना करें। / \(130^\circ=\frac{13\pi}{18}\), so (k=13). In exams, compare using \(180^\circ=\pi\).
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Through how many radians does the hour hand rotate in (5) hours (20) minutes?
A. \(\frac{8\pi}{9}\)
(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। / (5) hours (20) minutes \(=\frac{16}{3}\) hours, which is \(\frac{4}{9}\) of (12) hours. The angle is \(\frac{4}{9}\times2\pi=\frac{8\pi}{9}\).
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What is the signed angle swept by the minute hand in (47) minutes in radians?
B. \(-\frac{47\pi}{30}\)
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। / 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.
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In which quadrant will the terminal side of \(\frac{13\pi}{15}\) radians lie?
D. दूसरा चतुर्थांशSecond quadrant
\(\frac{13\pi}{15}=156^\circ\), जो \(90^\circ\) और \(180^\circ\) के बीच है। परीक्षा में चतुर्थांश तय करने से पहले डिग्री में बदलना आसान होता है। / \(\frac{13\pi}{15}=156^\circ\), which is between \(90^\circ\) and \(180^\circ\). In exams, converting to degrees often makes quadrant identification easier.
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If \(x^\circ=\frac{7\pi}{20}\) radians, what is the value of (x)?
C. (63)
\(\frac{7\pi}{20}\times\frac{180^\circ}{\pi}=63^\circ\), इसलिए (x=63) है। परीक्षा में \(\pi\) को काटकर सरल करें। / \(\frac{7\pi}{20}\times\frac{180^\circ}{\pi}=63^\circ\), so (x=63). In exams, cancel \(\pi\) and simplify.
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What is the radian measure of an angle \(15^\circ\) less than \(\frac{\pi}{3}\) radians?
B. \(\frac{\pi}{4}\)
\(\frac{\pi}{3}=60^\circ\), इसलिए नया कोण \(45^\circ=\frac{\pi}{4}\) है। परीक्षा में मिश्रित इकाइयों को एक ही इकाई में बदलें। / \(\frac{\pi}{3}=60^\circ\), so the new angle is \(45^\circ=\frac{\pi}{4}\). In exams, convert mixed units into one unit.
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Taking \(\pi=\frac{22}{7}\), what is the approximate degree measure of (2) radians?
A. \(114\frac{6}{11}^\circ\)
\(2\times\frac{180^\circ}{\pi}=2\times\frac{180^\circ\times7}{22}=114\frac{6}{11}^\circ\) है। परीक्षा में दिए गए \(\pi\) के मान का ही प्रयोग करें। / \(2\times\frac{180^\circ}{\pi}=2\times\frac{180^\circ\times7}{22}=114\frac{6}{11}^\circ\). In exams, use the given value of \(\pi\).
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How many radians are equal to \(1^\circ\)?
D. \(\frac{\pi}{180}\)
क्योंकि \(180^\circ=\pi\) रेडियन, इसलिए \(1^\circ=\frac{\pi}{180}\) रेडियन है। परीक्षा में इस मूल रूपांतरण को याद रखें। / Since \(180^\circ=\pi\) radians, \(1^\circ=\frac{\pi}{180}\) radians. Remember this basic conversion for exams.
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If arc length is (35) cm and radius is (14) cm, what is the central angle in radians?
D. \(\frac{5}{2}\)
सूत्र \(s=r\theta\) से \(\theta=\frac{35}{14}=\frac{5}{2}\) रेडियन है। परीक्षा में चाप लंबाई को त्रिज्या से भाग दें। / Using \(s=r\theta\), \(\theta=\frac{35}{14}=\frac{5}{2}\) radians. In exams, divide arc length by radius.
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What is the degree measure of \(-\frac{17\pi}{18}\) radians?
C. \(-170^\circ\)
\(-\frac{17\pi}{18}\) को \(180^\circ/\pi\) से गुणा करने पर \(-170^\circ\) मिलता है। ऋण चिह्न दिशा बताता है। / Multiplying \(-\frac{17\pi}{18}\) by \(180^\circ/\pi\) gives \(-170^\circ\). The negative sign shows direction.
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What is the degree measure of \(\frac{7\pi}{12}\) radians?
C. \(105^\circ\)
रेडियन को \(180^\circ/\pi\) से गुणा करने पर \(105^\circ\) मिलता है। परीक्षा में \(\pi\) को सीधे काटें। / Multiplying radians by \(180^\circ/\pi\) gives \(105^\circ\). In exams, cancel \(\pi\) directly.
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If \(\pi=\frac{22}{7}\) and (5) radians are converted into degrees what is the approximate value?
B. \(286^\circ21'49''\)
(5) रेडियन \(=5\times\frac{180^\circ}{\pi}\) है। \(\pi=\frac{22}{7}\) रखने पर लगभग \(286^\circ21'49''\) मिलता है। / (5) radians \(=5\times\frac{180^\circ}{\pi}\). Using \(\pi=\frac{22}{7}\) gives approximately \(286^\circ21'49''\).
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C. \(4080^\circ\)
(11) चक्कर \(3960^\circ\) और \(\frac{2\pi}{3}=120^\circ\) है। कुल कोण \(4080^\circ\) होगा। / (11) revolutions are \(3960^\circ\) and \(\frac{2\pi}{3}=120^\circ\). The total angle is \(4080^\circ\).
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Through how many radians does the hour hand turn from (1:20) to (6:50)?
B. \(\frac{11\pi}{12}\)
समय अंतर \(\frac{11}{2}\) घंटे है और घंटे की सुई \(30^\circ\) प्रति घंटा घूमती है। कुल कोण \(165^\circ=\frac{11\pi}{12}\) है। / The time difference is \(\frac{11}{2}\) hours and the hour hand turns \(30^\circ\) per hour. The total angle is \(165^\circ=\frac{11\pi}{12}\).
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Through how many radians does the minute hand turn from (4:12) to (4:47)?
C. \(\frac{7\pi}{6}\)
समय अंतर (35) मिनट है। कोण \(\frac{35}{60}\times2\pi=\frac{7\pi}{6}\) रेडियन है। / The time difference is (35) minutes. The angle is \(\frac{35}{60}\times2\pi=\frac{7\pi}{6}\) radians.
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B. (2)
\(75^\circ=\frac{5\pi}{12}\) है और \(\frac{53\pi}{12}=4\pi+\frac{5\pi}{12}\)। \(4\pi\) में (2) पूर्ण चक्कर होते हैं। / \(75^\circ=\frac{5\pi}{12}\) and \(\frac{53\pi}{12}=4\pi+\frac{5\pi}{12}\). \(4\pi\) contains (2) complete revolutions.
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Convert the angle \(18^\circ24'\) into radians.
B. \(\frac{23\pi}{225}\)
\(18^\circ24'=\frac{92}{5}^\circ\) है। रेडियन में \(\frac{92}{5}\times\frac{\pi}{180}=\frac{23\pi}{225}\) होगा। / \(18^\circ24'=\frac{92}{5}^\circ\). In radians it is \(\frac{92}{5}\times\frac{\pi}{180}=\frac{23\pi}{225}\).
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B. \(\frac{\pi}{4}\)
(\frac{\pi}{2}-x=\frac{1}{3}\(\pi-x\)) रखें। इससे \(x=\frac{\pi}{4}\) मिलता है। / Set (\frac{\pi}{2}-x=\frac{1}{3}\(\pi-x\)). This gives \(x=\frac{\pi}{4}\).
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C. (20) सेकंड(20) seconds
\(240^\circ=\frac{4\pi}{3}\) रेडियन है। समय \(\frac{4\pi/3}{\pi/15}=20\) सेकंड होगा। / \(240^\circ=\frac{4\pi}{3}\) radians. Time is \(\frac{4\pi/3}{\pi/15}=20\) seconds.
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Through how many radians will the second hand turn in (2) minutes (15) seconds?
C. \(\frac{9\pi}{2}\)
सेकंड सुई (60) सेकंड में \(2\pi\) घूमती है। (135) सेकंड में कोण \(\frac{9\pi}{2}\) है। / The second hand turns \(2\pi\) in (60) seconds. In (135) seconds the angle is \(\frac{9\pi}{2}\).
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Which value is correct when \(125^\circ15'30''\) is converted into radians?
A. \(\frac{15031\pi}{21600}\)
\(125^\circ15'30''=\frac{450930}{3600}^\circ\) है। इसे \(\frac{\pi}{180}\) से गुणा करने पर \(\frac{15031\pi}{21600}\) मिलता है। / \(125^\circ15'30''=\frac{450930}{3600}^\circ\). Multiplying by \(\frac{\pi}{180}\) gives \(\frac{15031\pi}{21600}\).
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A sector has perimeter (32) cm and arc length (12) cm. What is its central angle in radians?
B. \(\frac{6}{5}\)
परिमाप (2r+s) है इसलिए (2r+12=32) से (r=10)। अब \(\theta=\frac{s}{r}=\frac{6}{5}\) है। / Perimeter is (2r+s) so (2r+12=32) gives (r=10). Now \(\theta=\frac{s}{r}=\frac{6}{5}\).
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Which value is obtained when the angle \(137^\circ30'\) is converted into radians?
B. \(\frac{55\pi}{72}\)
\(137^\circ30'=\frac{275}{2}^\circ\) होता है। रेडियन के लिए \(\frac{\pi}{180}\) से गुणा करें। / \(137^\circ30'=\frac{275}{2}^\circ\). Multiply by \(\frac{\pi}{180}\) for radians.
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If (3) radians and \(x^\circ\) together form a straight angle, what is the value of (x)?
A. (\frac{180\(\pi-3\)}{\pi})
सीधा कोण \(\pi\) रेडियन होता है, इसलिए शेष कोण \(\pi-3\) रेडियन है। डिग्री में यह (\frac{180\(\pi-3\)}{\pi}) होगा। / A straight angle is \(\pi\) radians, so the remaining angle is \(\pi-3\) radians. In degrees, it is (\frac{180\(\pi-3\)}{\pi}).
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Which value is obtained when \(218^\circ24'\) is converted into radians?
A. \(\frac{91\pi}{75}\)
\(218^\circ24'=218.4^\circ=\frac{1092}{5}^\circ\), इसलिए रेडियन \(\frac{91\pi}{75}\) है। परीक्षा में (24') को \(0.4^\circ\) में बदलें। / \(218^\circ24'=218.4^\circ=\frac{1092}{5}^\circ\), so the radian measure is \(\frac{91\pi}{75}\). In exams, convert (24') into \(0.4^\circ\).
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If \(\frac{3x\pi}{20}\) radians equals \(81^\circ\), what is the value of (x)?
B. (3)
\(81^\circ=\frac{9\pi}{20}\), इसलिए \(\frac{3x\pi}{20}=\frac{9\pi}{20}\) से (x=3)। परीक्षा में दोनों कोणों को समान इकाई में लिखें। / \(81^\circ=\frac{9\pi}{20}\), so \(\frac{3x\pi}{20}=\frac{9\pi}{20}\) gives (x=3). In exams, write both angles in the same unit.
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If \(x^\circ=\frac{11\pi}{36}\) radians, what is the value of (x)?
D. (55)
\(\frac{11\pi}{36}\times\frac{180^\circ}{\pi}=55^\circ\)। परीक्षा में \(\pi\) को पहले काटें। / \(\frac{11\pi}{36}\times\frac{180^\circ}{\pi}=55^\circ\). In exams, cancel \(\pi\) first.
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A. \(675^\circ\)
कोण \(\frac{3\pi}{8}\times10=\frac{15\pi}{4}\) रेडियन है, जो \(675^\circ\) है। परीक्षा में पहले कुल रेडियन निकालें। / The angle is \(\frac{3\pi}{8}\times10=\frac{15\pi}{4}\) radians, which is \(675^\circ\). In exams, first find the total radians.
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If angular speed is \(15^\circ\) per second, what is it in radians per minute?
C. \(5\pi\)
\(15^\circ\) प्रति सेकंड से \(900^\circ\) प्रति मिनट मिलता है, और \(900^\circ=5\pi\) रेडियन है। परीक्षा में समय इकाई पहले बदलें। / \(15^\circ\) per second gives \(900^\circ\) per minute, and \(900^\circ=5\pi\) radians. In exams, convert the time unit first.
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A sector has arc length (25) cm and area (100) square cm. What is its central angle in radians?
B. \(\frac{25}{8}\)
\(A=\frac{1}{2}rs\) से (r=8), फिर \(\theta=\frac{s}{r}=\frac{25}{8}\)। परीक्षा में चाप और क्षेत्रफल से पहले त्रिज्या निकालें। / 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.
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In which quadrant is the angle \(\frac{9}{5}\) radians located?
C. दूसरा चतुर्थांशSecond quadrant
\(\frac{\pi}{2}<\frac{9}{5}<\pi\), इसलिए कोण दूसरे चतुर्थांश में है। परीक्षा में \(\frac{\pi}{2}\approx1.57\) और \(\pi\approx3.14\) से तुलना करें। / 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 \(\pi\approx3.14\).
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A. \(28\pi\)
पहिए की परिधि \(70\pi=220\) सेमी है, इसलिए चक्कर (14) होंगे। कुल कोण \(14\times2\pi=28\pi\) रेडियन है। / The wheel circumference is \(70\pi=220\) cm, so it makes (14) revolutions. The total angle is \(14\times2\pi=28\pi\) radians.
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If \(300^\circ=\frac{p\pi}{9}\) radians, what is the value of (p)?
D. (15)
\(300^\circ=\frac{5\pi}{3}=\frac{15\pi}{9}\), इसलिए (p=15)। परीक्षा में डिग्री से रेडियन बदलकर समान 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.
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If \(126^\circ=\frac{m\pi}{20}\) radians, what is the value of (m)?
C. (14)
\(126^\circ=\frac{126\pi}{180}=\frac{7\pi}{10}=\frac{14\pi}{20}\), इसलिए (m=14)। परीक्षा में दिए रूप जैसा हर बनाएं। / \(126^\circ=\frac{126\pi}{180}=\frac{7\pi}{10}=\frac{14\pi}{20}\), so (m=14). In exams, make the denominator match the given form.
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If a sector has arc length (16) cm and central angle (4) radians, what is its area?
A. (32) वर्ग सेमी(32) square cm
\(s=r\theta\) से (r=4), फिर \(A=\frac{1}{2}r^2\theta=32\)। परीक्षा में पहले त्रिज्या निकालकर क्षेत्रफल लगाएं। / 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.
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A sector has radius (7) cm and perimeter (22) cm. What is the central angle in radians?
B. \(\frac{8}{7}\)
सेक्टर परिमाप \(2r+r\theta\) होता है, इसलिए \(14+7\theta=22\)। इससे \(\theta=\frac{8}{7}\) मिलता है। / Sector perimeter is \(2r+r\theta\), so \(14+7\theta=22\). This gives \(\theta=\frac{8}{7}\).
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Through how many radians does the hour hand of a clock rotate in (5) hours (36) minutes?
D. \(\frac{14\pi}{15}\)
(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। / (5) hours (36) minutes \(=\frac{28}{5}\) hours and the hour hand rate is \(\frac{\pi}{6}\) radians per hour. Hence the angle is \(\frac{28}{5}\times\frac{\pi}{6}=\frac{14\pi}{15}\).
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Through how many radians does the minute hand of a clock rotate in (29) minutes?
B. \(\frac{29\pi}{30}\)
मिनट सुई (60) मिनट में \(2\pi\) घूमती है, इसलिए (29) मिनट में \(\frac{29\pi}{30}\) घूमेगी। परीक्षा में समय का अनुपात लगाएं। / 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.
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Which value is obtained when \(18^\circ45'\) is converted into radians?
A. \(\frac{5\pi}{48}\)
\(18^\circ45'=\frac{75}{4}^\circ\) और रेडियन मान \(\frac{75\pi}{720}=\frac{5\pi}{48}\) है। परीक्षा में मिनट को पहले डिग्री में बदलें। / \(18^\circ45'=\frac{75}{4}^\circ\) and the radian measure is \(\frac{75\pi}{720}=\frac{5\pi}{48}\). In exams, first convert minutes into degrees.
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What is the approximate degree measure of (4) radians?
C. \(229.2^\circ\)
(4) रेडियन \(=4\times\frac{180^\circ}{\pi}\approx229.2^\circ\) है। अनुमान में \(\pi\approx3.14\) रखें। / (4) radians \(=4\times\frac{180^\circ}{\pi}\approx229.2^\circ\). Use \(\pi\approx3.14\) for approximation.
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\(\frac{7\pi}{2}\) radians is equal to how many revolutions?
C. \(\frac{7}{4}\)
एक चक्कर \(2\pi\) रेडियन होता है। \(\frac{7\pi}{2}\div2\pi=\frac{7}{4}\) चक्कर। / One revolution is \(2\pi\) radians. \(\frac{7\pi}{2}\div2\pi=\frac{7}{4}\) revolutions.
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Through how many radians does the minute hand turn in (7.5) minutes?
B. \(\frac{\pi}{4}\)
(60) मिनट में \(2\pi\) रेडियन घूमती है। (7.5) मिनट में \(\frac{7.5}{60}\times2\pi=\frac{\pi}{4}\) है। / It turns \(2\pi\) radians in (60) minutes. In (7.5) minutes it turns \(\frac{7.5}{60}\times2\pi=\frac{\pi}{4}\).
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How many degrees are equal to \(\frac{\pi}{9}\) radians?
B. \(20^\circ\)
\(\frac{\pi}{9}\times\frac{180^\circ}{\pi}=20^\circ\) है। रेडियन से डिग्री में जाने पर \(\frac{180}{\pi}\) से गुणा करें। / \(\frac{\pi}{9}\times\frac{180^\circ}{\pi}=20^\circ\). Multiply by \(\frac{180}{\pi}\) to convert radians into degrees.
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Convert the angle \(54^\circ\) into radians.
A. \(\frac{3\pi}{10}\)
\(54^\circ\times\frac{\pi}{180}=\frac{3\pi}{10}\) होता है। डिग्री से रेडियन में जाने पर \(\frac{\pi}{180}\) लगाएं। / \(54^\circ\times\frac{\pi}{180}=\frac{3\pi}{10}\). Use \(\frac{\pi}{180}\) when converting degrees to radians.
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If an angle is \(\frac{2}{5}\) radians then what is its complement?
A. \(\frac{\pi}{2}-\frac{2}{5}\)
रेडियन में पूरक कोणों का योग \(\frac{\pi}{2}\) होता है। इसलिए उत्तर \(\frac{\pi}{2}-\frac{2}{5}\) है। / In radians complementary angles add to \(\frac{\pi}{2}\). So the answer is \(\frac{\pi}{2}-\frac{2}{5}\).
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Through how many radians does the minute hand of a clock turn in (25) minutes?
C. \(\frac{5\pi}{6}\)
मिनट सुई (60) मिनट में \(2\pi\) घूमती है। (25) मिनट में कोण \(\frac{25}{60}\times2\pi=\frac{5\pi}{6}\) है। / The minute hand turns \(2\pi\) in (60) minutes. In (25) minutes the angle is \(\frac{25}{60}\times2\pi=\frac{5\pi}{6}\).
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If angular speed is (9) revolutions per minute then what is its value in radians per second?
B. \(\frac{3\pi}{10}\)
(9) चक्कर प्रति मिनट \(=18\pi\) रेडियन प्रति मिनट है। (60) से भाग देने पर \(\frac{3\pi}{10}\) मिलता है। / (9) revolutions per minute equals \(18\pi\) radians per minute. Dividing by (60) gives \(\frac{3\pi}{10}\).
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Which value is obtained when the angle \(150^\circ\) is converted into radians?
C. \(\frac{5\pi}{6}\)
डिग्री को रेडियन में बदलने के लिए \( \frac{\pi}{180} \) से गुणा करते हैं। परीक्षा में \(30^\circ\) के गुणकों को जल्दी पहचानें। / Multiply degrees by \( \frac{\pi}{180} \) to convert into radians. In exams identify multiples of \(30^\circ\) quickly.
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If a sector with angle (2) radians has arc length (18) cm, what is its area?
B. (81) वर्ग सेमी(81) square cm
\(s=r\theta\) से (r=9), फिर \(A=\frac{1}{2}r^2\theta=81\)। परीक्षा में पहले त्रिज्या निकालें। / From \(s=r\theta\), (r=9), then \(A=\frac{1}{2}r^2\theta=81\). In exams, find the radius first.
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If an angle is \(\frac{4}{3}\) radians, what is its nearest whole number measure in degrees?
B. \(76^\circ\)
\(\frac{4}{3}\times\frac{180^\circ}{\pi}\approx76.4^\circ\), इसलिए निकटतम \(76^\circ\) है। परीक्षा में \(\pi\approx3.14\) लेकर अनुमान लगाएं। / \(\frac{4}{3}\times\frac{180^\circ}{\pi}\approx76.4^\circ\), so the nearest value is \(76^\circ\). In exams, use \(\pi\approx3.14\) for approximation.
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If \(245^\circ\) is written in radians as \(\frac{m\pi}{36}\), what is the value of (m)?
C. (49)
\(245^\circ=\frac{245\pi}{180}=\frac{49\pi}{36}\), इसलिए (m=49)। परीक्षा में हर को दिए हुए रूप जैसा बनाइए। / \(245^\circ=\frac{245\pi}{180}=\frac{49\pi}{36}\), so (m=49). In exams, make the denominator match the given form.
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If \(\frac{11\pi}{9}\) radians is converted into degrees, in which quadrant will the angle lie?
C. तीसरा चतुर्थांशThird quadrant
\(\frac{11\pi}{9}\times\frac{180^\circ}{\pi}=220^\circ\), जो तीसरे चतुर्थांश में है। परीक्षा में डिग्री में बदलकर चतुर्थांश पहचानना आसान होता है। / \(\frac{11\pi}{9}\times\frac{180^\circ}{\pi}=220^\circ\), which lies in the third quadrant. In exams, converting to degrees can make quadrant identification easier.
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If \(72^\circ\) is converted into radians and written as \(\frac{k\pi}{5}\), what is (k)?
B. (2)
\(72^\circ=\frac{72\pi}{180}=\frac{2\pi}{5}\), इसलिए (k=2)। परीक्षा में अंश को सरल रूप में जरूर करें। / \(72^\circ=\frac{72\pi}{180}=\frac{2\pi}{5}\), so (k=2). In exams, always simplify the fraction.
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If (x) revolutions equal \(\frac{15\pi}{2}\) radians, what is (x)?
A. \(\frac{15}{4}\)
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। / One revolution is \(2\pi\) radians, so \(x=\frac{15\pi}{2}\div2\pi=\frac{15}{4}\). In exams, divide radians by \(2\pi\).
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Through how many radians does the hour hand of a clock rotate in (2) hours (40) minutes?
A. \(\frac{4\pi}{9}\)
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। / The hour hand rotates \(2\pi\) in (12) hours, and (2) hours (40) minutes \(=\frac{8}{3}\) hours. The angle is \(\frac{8}{3}\times\frac{\pi}{6}=\frac{4\pi}{9}\).
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If \(a^\circ\) and \(\frac{7\pi}{12}\) radians represent the same angle, what is (a)?
C. (105)
\(\frac{7\pi}{12}\times\frac{180^\circ}{\pi}=105^\circ\)। परीक्षा में रेडियन से डिग्री में बदलते समय \(\pi\) काटें। / \(\frac{7\pi}{12}\times\frac{180^\circ}{\pi}=105^\circ\). In exams, cancel \(\pi\) while converting radians to degrees.
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If \(132^\circ 30'\) is converted into radians, what is the correct form?
A. \(\frac{53\pi}{72}\)
\(132^\circ 30'=132.5^\circ=\frac{265}{2}^\circ\), इसलिए रेडियन \(\frac{265\pi}{360}=\frac{53\pi}{72}\)। परीक्षा में मिनट को दशमलव डिग्री में बदलें। / \(132^\circ 30'=132.5^\circ=\frac{265}{2}^\circ\), so radians are \(\frac{265\pi}{360}=\frac{53\pi}{72}\). In exams, convert minutes into decimal degrees.
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If an angle is (3.9) radians, in which quadrant is it located?
C. तीसरा चतुर्थांशThird quadrant
\(\pi<3.9<\frac{3\pi}{2}\), इसलिए कोण तीसरे चतुर्थांश में है। परीक्षा में \(\pi\approx3.14\) और \(\frac{3\pi}{2}\approx4.71\) से तुलना करें। / Since \(\pi<3.9<\frac{3\pi}{2}\), the angle is in the third quadrant. In exams, compare with \(\pi\approx3.14\) and \(\frac{3\pi}{2}\approx4.71\).
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If a wheel makes (45) revolutions, through how many radians does it rotate?
C. \(90\pi\)
एक चक्कर \(2\pi\) रेडियन होता है, इसलिए (45) चक्कर \(90\pi\) रेडियन होंगे। परीक्षा में चक्कर को \(2\pi\) से गुणा करें। / One revolution is \(2\pi\) radians, so (45) revolutions are \(90\pi\) radians. In exams, multiply revolutions by \(2\pi\).
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In which quadrant will the terminal side of \(\frac{19\pi}{6}\) radians lie?
B. दूसरा चतुर्थांशSecond quadrant
\(\frac{19\pi}{6}-2\pi=\frac{7\pi}{6}\) 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। / \(\frac{19\pi}{6}-2\pi=\frac{7\pi}{6}\), which lies in the third quadrant. In exams, reduce the angle before identifying the quadrant.
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In which quadrant does the angle (2.35) radians lie?
B. दूसरा चतुर्थांशSecond quadrant
\(\frac{\pi}{2}<2.35<\pi\), इसलिए कोण दूसरे चतुर्थांश में है। परीक्षा में रेडियन सीमाएं \(\frac{\pi}{2}\), \(\pi\), \(\frac{3\pi}{2}\) से तुलना करें। / Since \(\frac{\pi}{2}<2.35<\pi\), the angle lies in the second quadrant. In exams, compare radians with \(\frac{\pi}{2}\), \(\pi\), and \(\frac{3\pi}{2}\).
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Through how many radians does the minute hand of a clock rotate in (17) minutes?
A. \(\frac{17\pi}{30}\)
मिनट सुई (60) मिनट में \(2\pi\) घूमती है, इसलिए (17) मिनट में \(\frac{17\pi}{30}\)। परीक्षा में समय अनुपात से कोण निकालें। / 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.
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If \(\frac{3\pi}{5}\) radians is converted into degrees, what is the angle?
B. \(108^\circ\)
\(\frac{3\pi}{5}\times\frac{180^\circ}{\pi}=108^\circ\)। परीक्षा में पहले \(\pi\) हटाकर गुणा करें। / \(\frac{3\pi}{5}\times\frac{180^\circ}{\pi}=108^\circ\). In exams, cancel \(\pi\) before multiplying.
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Which value is obtained when \(225^\circ\) is converted into radians?
C. \(\frac{5\pi}{4}\)
डिग्री को रेडियन में बदलने के लिए \(\frac{\pi}{180}\) से गुणा करें। परीक्षा में (225) और (180) को (45) से काटें। / Multiply by \(\frac{\pi}{180}\) to convert degrees into radians. In exams, cancel (225) and (180) by (45).
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A sector has area (24) square cm and radius (6) cm. What is the central angle in radians?
B. \(\frac{4}{3}\)
सेक्टर क्षेत्रफल \(A=\frac{1}{2}r^2\theta\), इसलिए \(24=18\theta\)। परीक्षा में क्षेत्रफल सूत्र में \(\theta\) रेडियन में ही लें। / Sector area is \(A=\frac{1}{2}r^2\theta\), so \(24=18\theta\). In exams, use \(\theta\) in radians in the area formula.
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If \(x^\circ=\frac{5\pi}{18}\) radians, what is the value of (x)?
B. (50)
रेडियन को डिग्री में बदलने के लिए \(\frac{180}{\pi}\) से गुणा करते हैं। परीक्षा में \(\pi\) कटाने पर गणना सरल होती है। / Multiply by \(\frac{180}{\pi}\) to convert radians into degrees. In exams, cancel \(\pi\) first to simplify calculation.
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If \(x^\circ=\frac{23\pi}{20}\) radians, what is the value of (x)?
A. \(207^\circ\)
\( \frac{23\pi}{20}\times\frac{180^\circ}{\pi}=207^\circ\) है। \(180^\circ\div20=9^\circ\) लेकर गुणा करें। / \( \frac{23\pi}{20}\times\frac{180^\circ}{\pi}=207^\circ\). Use \(180^\circ\div20=9^\circ\) and multiply.
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If \( \frac{x\pi}{18} \) radians is equal to \(250^\circ\), what is (x)?
C. (25)
\(250^\circ=\frac{25\pi}{18}\) है इसलिए (x=25) है। डिग्री को रेडियन में बदलकर तुलना करें। / \(250^\circ=\frac{25\pi}{18}\), so (x=25). Convert degrees to radians and compare.
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C. (16) सेमी(16) cm
\(r=\frac{s}{\theta}=\frac{12\pi}{3\pi/4}=16\) सेमी है। \(s=r\theta\) को उल्टा लगाएं। / \(r=\frac{s}{\theta}=\frac{12\pi}{3\pi/4}=16\) cm. Use \(s=r\theta\) in reverse.
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If \(x^\circ\) and \( \frac{7\pi}{9} \) radians are complementary, what is the value of (x)?
D. कोई धनात्मक मान नहींNo positive value
\( \frac{7\pi}{9}=140^\circ \) है जो \(90^\circ\) से बड़ा है इसलिए धनात्मक संपूरक कोण संभव नहीं है। पहले इकाई समान करें। / \( \frac{7\pi}{9}=140^\circ \), which is greater than \(90^\circ\), so no positive complementary angle is possible. First make the units same.
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A. \( \frac{\pi}{4} \)
\( \frac{9\pi}{4}-2\pi=\frac{\pi}{4} \) है। \(2\pi\) घटाकर सहसमापी मानक कोण पाएं। / \( \frac{9\pi}{4}-2\pi=\frac{\pi}{4} \). Subtract \(2\pi\) to find the coterminal standard angle.
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What is \( \frac{7\pi}{18} \) radians in degrees and minutes?
A. \(70^\circ\)
\( \frac{7\pi}{18}\times\frac{180^\circ}{\pi}=70^\circ \) है। रेडियन से डिग्री में \( \frac{180^\circ}{\pi} \) से गुणा करें। / \( \frac{7\pi}{18}\times\frac{180^\circ}{\pi}=70^\circ \). Multiply by \( \frac{180^\circ}{\pi} \) to convert radians to degrees.
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A wheel turns (42) radians in (7) seconds. Through how many degrees will it turn in (3) seconds?
A. \( \frac{1080^\circ}{\pi} \)
दर (6) रेडियन प्रति सेकंड है इसलिए (3) सेकंड में (18) रेडियन यानी \(18\cdot\frac{180^\circ}{\pi}=\frac{3240^\circ}{\pi}\) है। / The rate is (6) radians per second, so in (3) seconds it turns (18) radians, which is \(18\cdot\frac{180^\circ}{\pi}=\frac{3240^\circ}{\pi}\).
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C. \(100^\circ\)
\( \frac{5}{3}\times\frac{180^\circ}{3}=100^\circ \) है। दिए गए \( \pi \) के अनुमान का ही उपयोग करें। / \( \frac{5}{3}\times\frac{180^\circ}{3}=100^\circ \). Use the approximation of \( \pi \) given in the question.
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For \( \frac{17\pi}{12} \) radians, which is the correct pair of reference angle and quadrant?
A. \( \frac{5\pi}{12} \) और तृतीय चतुर्थांश\( \frac{5\pi}{12} \) and third quadrant
\( \frac{17\pi}{12} \) \( \pi \) और \( \frac{3\pi}{2} \) के बीच है और संदर्भ कोण \( \frac{17\pi}{12}-\pi=\frac{5\pi}{12} \) है। चतुर्थांश के अनुसार सूत्र बदलता है। / \( \frac{17\pi}{12} \) lies between \( \pi \) and \( \frac{3\pi}{2} \), and the reference angle is \( \frac{17\pi}{12}-\pi=\frac{5\pi}{12} \). The formula changes by quadrant.
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If \( \theta=\frac{5\pi}{18} \), what is its complementary angle in radians?
A. \( \frac{2\pi}{9} \)
संपूरक कोणों का योग \( \frac{\pi}{2} \) होता है इसलिए \( \frac{\pi}{2}-\frac{5\pi}{18}=\frac{2\pi}{9} \) है। समान हर बनाकर घटाएं। / Complementary angles sum to \( \frac{\pi}{2} \), so \( \frac{\pi}{2}-\frac{5\pi}{18}=\frac{2\pi}{9} \). Use a common denominator before subtracting.
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If \( \theta=\frac{7\pi}{12} \), what is its supplementary angle in radians?
A. \( \frac{5\pi}{12} \)
पूरक कोणों का योग \( \pi \) होता है इसलिए \( \pi-\frac{7\pi}{12}=\frac{5\pi}{12} \) है। रेडियन में \(180^\circ\) की जगह \( \pi \) लें। / Supplementary angles sum to \( \pi \), so \( \pi-\frac{7\pi}{12}=\frac{5\pi}{12} \). In radians use \( \pi \) instead of \(180^\circ\).
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Through how many radians does the minute hand of a clock turn in (18) minutes?
C. \( \frac{3\pi}{5} \) रेडियन\( \frac{3\pi}{5} \) radians
मिनट सुई (60) मिनट में \(2\pi\) घूमती है इसलिए (18) मिनट में \( \frac{18}{60}\cdot2\pi=\frac{3\pi}{5} \) है। समय का अनुपात पूर्ण चक्कर से लगाएं। / The minute hand turns \(2\pi\) in (60) minutes, so in (18) minutes it turns \( \frac{18}{60}\cdot2\pi=\frac{3\pi}{5} \). Use the time fraction of one full revolution.
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If arc (s=22) cm and sector area (A=121) square cm, what is the central angle in radians?
B. (2) रेडियन(2) radians
\(A=\frac{1}{2}rs\) से \(121=\frac{1}{2}r\cdot22\) इसलिए (r=11) और \( \theta=\frac{s}{r}=2 \) है। चाप और क्षेत्रफल साथ दिए हों तो पहले (r) निकालें। / Using \(A=\frac{1}{2}rs\), \(121=\frac{1}{2}r\cdot22\), so (r=11) and \( \theta=\frac{s}{r}=2 \). When arc and area are given, find (r) first.
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In which quadrant does \( \frac{19\pi}{7} \) radians lie?
C. तृतीय चतुर्थांशThird quadrant
\( \frac{19\pi}{7}-2\pi=\frac{5\pi}{7} \) है और यह \( \frac{\pi}{2} \) तथा \( \pi \) के बीच है? सावधानी से \( \frac{5\pi}{7} \) द्वितीय चतुर्थांश में है। / \( \frac{19\pi}{7}-2\pi=\frac{5\pi}{7} \), and \( \frac{5\pi}{7} \) lies in the second quadrant. Always reduce the angle before deciding the quadrant.
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Which value is obtained by converting \( \frac{37\pi}{15} \) radians into degrees?
B. \(444^\circ\)
\( \frac{37\pi}{15}\times\frac{180^\circ}{\pi}=444^\circ\) है। हर (15) हो तो \(180^\circ\div15=12^\circ\) लें। / \( \frac{37\pi}{15}\times\frac{180^\circ}{\pi}=444^\circ\). If the denominator is (15), use \(180^\circ\div15=12^\circ\).
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On which axis will the terminal side of \( \frac{15\pi}{2} \) radians lie?
D. ऋणात्मक (y)-अक्षNegative (y)-axis
\( \frac{15\pi}{2}-6\pi=\frac{3\pi}{2} \) है और \( \frac{3\pi}{2} \) ऋणात्मक (y)-अक्ष पर है। \(2\pi\) के गुणज घटाकर अक्ष पहचानें। / \( \frac{15\pi}{2}-6\pi=\frac{3\pi}{2} \), and \( \frac{3\pi}{2} \) lies on the negative (y)-axis. Subtract multiples of \(2\pi\) to identify the axis.
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If the sector area is (54) square cm and (r=6) cm, what is the central angle in radians?
B. (3) रेडियन(3) radians
\(54=\frac{1}{2}\times36\times\theta\) से \( \theta=3 \) रेडियन है। क्षेत्रफल सूत्र में अज्ञात कोण को अलग करें। / From \(54=\frac{1}{2}\times36\times\theta\), \( \theta=3 \) radians. Isolate the unknown angle in the sector area formula.
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C. \(70\pi\) वर्ग सेमी\(70\pi\) square cm
क्षेत्रफल \( \frac{1}{2}r^2\theta=\frac{1}{2}\times196\times\frac{5\pi}{7}=70\pi \) है। रेडियन कोण के साथ यह सूत्र सीधे लगाएं। / Area is \( \frac{1}{2}r^2\theta=\frac{1}{2}\times196\times\frac{5\pi}{7}=70\pi \). Use this formula directly with a radian angle.
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If arc (s=18) cm and angle \( \theta=\frac{3}{4} \) radians, what is the radius?
C. (24) सेमी(24) cm
\(r=\frac{s}{\theta}=\frac{18}{3/4}=24\) सेमी है। \(s=r\theta\) में (r) को अलग करें। / \(r=\frac{s}{\theta}=\frac{18}{3/4}=24\) cm. Isolate (r) in \(s=r\theta\).
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If (r=16) cm and \( \theta=\frac{5\pi}{8} \) radians, what will be the arc length?
C. \(10\pi\) सेमी\(10\pi\) cm
\(s=r\theta=16\times\frac{5\pi}{8}=10\pi\) सेमी है। कोण रेडियन में हो तो \(s=r\theta\) सीधे लागू होता है। / \(s=r\theta=16\times\frac{5\pi}{8}=10\pi\) cm. When the angle is in radians, \(s=r\theta\) applies directly.
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When (0.75) radians is approximately converted into degrees, the value is closest to which option?
B. \(43.0^\circ\)
\(0.75\times57.3^\circ\approx43.0^\circ\) है। छोटे रेडियन मानों के लिए भी वही रूपांतरण कारक लगता है। / \(0.75\times57.3^\circ\approx43.0^\circ\). The same conversion factor applies for small radian values too.
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When (2.8) radians is approximately converted into degrees, which value is nearest?
C. \(160.4^\circ\)
\(2.8\times57.3^\circ\approx160.4^\circ\) है। अनुमान में (1) रेडियन को \(57.3^\circ\) मानें। / \(2.8\times57.3^\circ\approx160.4^\circ\). For estimation take (1) radian as \(57.3^\circ\).
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In which quadrant does \( \frac{15\pi}{11} \) radians lie?
C. तृतीय चतुर्थांशThird quadrant
\( \pi<\frac{15\pi}{11}<\frac{3\pi}{2} \) है इसलिए यह तृतीय चतुर्थांश में आता है। \( \pi \) के बाद और \( \frac{3\pi}{2} \) से पहले तीसरा चतुर्थांश होता है।
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In which quadrant will the terminal side of \( \frac{6\pi}{11} \) radians lie?
B. द्वितीय चतुर्थांशSecond quadrant
\( \frac{\pi}{2}<\frac{6\pi}{11}<\pi \) है इसलिए अंतिम भुजा द्वितीय चतुर्थांश में है। \( \frac{\pi}{2} \) और \( \pi \) के बीच दूसरा चतुर्थांश होता है।
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In which quadrant does \( \frac{23\pi}{14} \) radians lie?
D. चतुर्थ चतुर्थांशFourth quadrant
\( \frac{3\pi}{2}<\frac{23\pi}{14}<2\pi \) है इसलिए यह चतुर्थ चतुर्थांश में है। रेडियन सीमाओं की तुलना समान हर से करें।
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Convert \(-\frac{9\pi}{8}\) radians into degrees.
D. \(-202.5^\circ\)
\(-\frac{9\pi}{8}\times\frac{180^\circ}{\pi}=-202.5^\circ\) है। ऋणात्मक रेडियन का चिह्न डिग्री में भी रहता है। / \(-\frac{9\pi}{8}\times\frac{180^\circ}{\pi}=-202.5^\circ\). The negative sign in radians remains in degrees.
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What is the degree measure of \( \frac{11\pi}{15} \) radians?
C. \(132^\circ\)
\( \frac{11\pi}{15}\times\frac{180^\circ}{\pi}=132^\circ\) है। \(180^\circ\div15=12^\circ\) करके गुणा करें। / \( \frac{11\pi}{15}\times\frac{180^\circ}{\pi}=132^\circ\). Calculate \(180^\circ\div15=12^\circ\) and multiply.
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How many degrees are equal to \( \frac{13\pi}{18} \) radians?
B. \(130^\circ\)
\( \frac{13\pi}{18}\times\frac{180^\circ}{\pi}=130^\circ\) होता है। हर (18) हो तो \(180^\circ\div18=10^\circ\) लें। / \( \frac{13\pi}{18}\times\frac{180^\circ}{\pi}=130^\circ\). If the denominator is (18), take \(180^\circ\div18=10^\circ\).
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What do we get by converting \( \frac{\pi}{20} \) radians into degrees?
A. \(9^\circ\)
\( \frac{\pi}{20}\times\frac{180^\circ}{\pi}=9^\circ\) है। हर से \(180^\circ\) को भाग दें। / \( \frac{\pi}{20}\times\frac{180^\circ}{\pi}=9^\circ\). Divide \(180^\circ\) by the denominator.
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