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658 questions tagged with trigonometric-functions.
In which quadrant does \( \frac{9\pi}{7} \) radians lie?
C. तृतीय चतुर्थांशThird quadrant
\( \pi<\frac{9\pi}{7}<\frac{3\pi}{2} \) इसलिए यह तृतीय चतुर्थांश में है। रेडियन सीमा से सीधे चतुर्थांश पहचानें।
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\( -710^\circ \) gives a coterminal angle in which quadrant?
A. प्रथम चतुर्थांशFirst quadrant
\( -710^\circ+720^\circ=10^\circ \) है इसलिए अंतिम भुजा प्रथम चतुर्थांश में है। बड़े ऋणात्मक कोण में \(360^\circ\) के गुणज जोड़ें। / \( -710^\circ+720^\circ=10^\circ \), so the terminal side lies in the first quadrant. Add multiples of \(360^\circ\) to a large negative angle.
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In which quadrant will the terminal side of \( -250^\circ \) lie?
B. द्वितीय चतुर्थांशSecond quadrant
\( -250^\circ+360^\circ=110^\circ \) है और \(110^\circ\) द्वितीय चतुर्थांश में है। पहले धनात्मक सहसमापी कोण निकालें। / \( -250^\circ+360^\circ=110^\circ \) and \(110^\circ\) lies in the second quadrant. First find the positive coterminal angle.
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What is the angle between (0) and \(2\pi\) for \( -\frac{25\pi}{8} \)?
C. \( \frac{7\pi}{8} \)
\( -\frac{25\pi}{8}+\frac{32\pi}{8}=\frac{7\pi}{8} \) है। हर समान रखकर \(2\pi\) जोड़ना सुरक्षित तरीका है। / \( -\frac{25\pi}{8}+\frac{32\pi}{8}=\frac{7\pi}{8} \). Keeping the same denominator is a safe method while adding \(2\pi\).
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Which is the principal coterminal angle of \( \frac{31\pi}{3} \)?
B. \( \frac{\pi}{3} \)
\( \frac{31\pi}{3}-\frac{30\pi}{3}=\frac{\pi}{3} \) है। \(2\pi=\frac{6\pi}{3}\) का गुणज घटाएं। / \( \frac{31\pi}{3}-\frac{30\pi}{3}=\frac{\pi}{3} \). Subtract a multiple of \(2\pi=\frac{6\pi}{3}\).
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What is the coterminal angle of \( -\frac{19\pi}{6} \) between (0) and \(2\pi\)?
B. \( \frac{5\pi}{6} \)
\( -\frac{19\pi}{6}+\frac{24\pi}{6}=\frac{5\pi}{6} \) है। ऋणात्मक रेडियन कोण में \(2\pi\) के गुणज जोड़ें। / \( -\frac{19\pi}{6}+\frac{24\pi}{6}=\frac{5\pi}{6} \). Add multiples of \(2\pi\) to a negative radian angle.
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What is the coterminal angle of \( \frac{29\pi}{4} \) between (0) and \(2\pi\)?
A. \( \frac{5\pi}{4} \)
\( \frac{29\pi}{4}-\frac{24\pi}{4}=\frac{5\pi}{4} \) है। रेडियन में \(2\pi=\frac{8\pi}{4}\) घटाते हैं। / \( \frac{29\pi}{4}-\frac{24\pi}{4}=\frac{5\pi}{4} \). In radians subtract \(2\pi=\frac{8\pi}{4}\).
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What is the principal coterminal angle of \( -1430^\circ \)?
D. \(10^\circ\)
\( -1430^\circ+1440^\circ=10^\circ \) है। निकटतम बड़े \(360^\circ\) के गुणज को जोड़ना आसान है। / \( -1430^\circ+1440^\circ=10^\circ \). Adding the nearest larger multiple of \(360^\circ\) is easy.
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What will be the principal angle of \(1540^\circ\)?
C. \(100^\circ\)
\(1540^\circ-1440^\circ=100^\circ\) है। मुख्य कोण सामान्यतः \(0^\circ\) से \(360^\circ\) के बीच लिया जाता है। / \(1540^\circ-1440^\circ=100^\circ\). The principal angle is usually taken between \(0^\circ\) and \(360^\circ\).
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Which is the coterminal angle of \( -1000^\circ \) between \(0^\circ\) and \(360^\circ\)?
B. \(80^\circ\)
\( -1000^\circ+1080^\circ=80^\circ \) है। ऋणात्मक बड़े कोणों में \(360^\circ\) के गुणज जोड़ें। / \( -1000^\circ+1080^\circ=80^\circ \). Add multiples of \(360^\circ\) for large negative angles.
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What is the coterminal angle of \(985^\circ\) between \(0^\circ\) and \(360^\circ\)?
A. \(265^\circ\)
\(985^\circ-720^\circ=265^\circ\) है। बड़े कोण से \(360^\circ\) के उपयुक्त गुणज घटाएं। / \(985^\circ-720^\circ=265^\circ\). Subtract a suitable multiple of \(360^\circ\) from a large angle.
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Convert \( \frac{13\pi}{8} \) radians into degrees.
D. \(292.5^\circ\)
\( \frac{13\pi}{8}\times \frac{180^\circ}{\pi}=292.5^\circ\) है। \( \frac{\pi}{8}=22.5^\circ \) को याद रखें। / \( \frac{13\pi}{8}\times \frac{180^\circ}{\pi}=292.5^\circ\). Remember \( \frac{\pi}{8}=22.5^\circ \).
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What is the degree measure of \( -\frac{7\pi}{6} \) radians?
C. \(-210^\circ\)
\( -\frac{7\pi}{6}\times \frac{180^\circ}{\pi}=-210^\circ\) होता है। रेडियन का ऋणात्मक चिह्न डिग्री में भी रहता है। / \( -\frac{7\pi}{6}\times \frac{180^\circ}{\pi}=-210^\circ\). The negative sign in radians remains in degrees.
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How many degrees are equal to \( \frac{5\pi}{24} \) radians?
B. \(37.5^\circ\)
\( \frac{5\pi}{24}\times \frac{180^\circ}{\pi}=37.5^\circ\) है। हर (24) हो तो \(180^\circ\div 24\) करें। / \( \frac{5\pi}{24}\times \frac{180^\circ}{\pi}=37.5^\circ\). If the denominator is (24), calculate \(180^\circ\div 24\).
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What do we get by converting \( \frac{3\pi}{8} \) radians into degrees?
A. \(67.5^\circ\)
\( \frac{3\pi}{8}\times \frac{180^\circ}{\pi}=67.5^\circ\) है। \(180^\circ\div 8=22.5^\circ\) करके गुणा करें। / \( \frac{3\pi}{8}\times \frac{180^\circ}{\pi}=67.5^\circ\). Divide \(180^\circ\) by (8) and then multiply.
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Which is the radian form of \(405^\circ\)?
D. \( \frac{9\pi}{4} \) रेडियन\( \frac{9\pi}{4} \) radians
\(405^\circ=\frac{405\pi}{180}=\frac{9\pi}{4}\) होता है। \(360^\circ\) से बड़े कोणों को भी उसी नियम से बदलें। / \(405^\circ=\frac{405\pi}{180}=\frac{9\pi}{4}\). Use the same rule even for angles greater than \(360^\circ\).
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Convert \(-225^\circ\) into radians.
C. \(-\frac{5\pi}{4}\) रेडियन\(-\frac{5\pi}{4}\) radians
\(-225^\circ=\frac{-225\pi}{180}=-\frac{5\pi}{4}\) है। ऋणात्मक कोण का चिह्न अंत तक बनाए रखें। / \(-225^\circ=\frac{-225\pi}{180}=-\frac{5\pi}{4}\). Keep the negative sign till the end.
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What is the radian measure of \(37.5^\circ\)?
B. \( \frac{5\pi}{24} \) रेडियन\( \frac{5\pi}{24} \) radians
\(37.5^\circ=\frac{37.5\pi}{180}=\frac{5\pi}{24}\) होता है। \(37.5^\circ\) को \( \frac{75^\circ}{2} \) मानकर भी हल कर सकते हैं। / \(37.5^\circ=\frac{37.5\pi}{180}=\frac{5\pi}{24}\). You can also treat \(37.5^\circ\) as \( \frac{75^\circ}{2} \).
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C. \(6\pi\) वर्ग सेमी\(6\pi\) square cm
त्रिज्यखंड क्षेत्रफल \( \frac{1}{2}r^2\theta \) से \( \frac{1}{2}\times36\times\frac{\pi}{3}=6\pi \) है। कोण रेडियन में हो तो सूत्र सीधे लगाएं। / The sector area is \( \frac{1}{2}r^2\theta \) so \( \frac{1}{2}\times36\times\frac{\pi}{3}=6\pi \). Apply the formula directly when the angle is in radians.
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A circle has radius (14) cm and central angle \( \frac{\pi}{7} \) radians. What is the arc length?
B. \(2\pi\) सेमी\(2\pi\) cm
\(s=r\theta=14\times \frac{\pi}{7}=2\pi\) सेमी है। रेडियन कोण के साथ \(s=r\theta\) सीधे लागू करें। / \(s=r\theta=14\times \frac{\pi}{7}=2\pi\) cm. Apply \(s=r\theta\) directly with a radian angle.
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In a circle the arc length is equal to the radius. What will be the angle at the centre?
A. (1) रेडियन(1) radian
यदि (s=r) है तो \( \theta=\frac{s}{r}=1 \) रेडियन है। यही रेडियन की मूल परिभाषा है। / If (s=r) then \( \theta=\frac{s}{r}=1 \) radian. This is the basic definition of a radian.
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Which angle has radian measure \( \frac{3}{2} \) if arc (s=18) cm and radius (r=12) cm?
D. \( \frac{3}{2} \) रेडियन\( \frac{3}{2} \) radians
\( \theta=\frac{s}{r}=\frac{18}{12}=\frac{3}{2} \) रेडियन है। चाप और त्रिज्या की इकाई समान होनी चाहिए। / \( \theta=\frac{s}{r}=\frac{18}{12}=\frac{3}{2} \) radians. The arc length and radius must have the same unit.
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If (s=9) cm and \( \theta=3 \) radians then what is the radius (r)?
C. (3) सेमी(3) cm
\(r=\frac{s}{\theta}=\frac{9}{3}=3\) सेमी है। \(s=r\theta\) में आवश्यक राशि को अलग करें। / \(r=\frac{s}{\theta}=\frac{9}{3}=3\) cm. Isolate the required quantity in \(s=r\theta\).
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What will be the arc length made by \(135^\circ\) in a circle of radius (8) cm?
B. \(6\pi\) सेमी\(6\pi\) cm
\(135^\circ=\frac{3\pi}{4}\) और \(s=8\times \frac{3\pi}{4}=6\pi\) सेमी है। डिग्री कोण को पहले रेडियन में बदलना जरूरी है। / \(135^\circ=\frac{3\pi}{4}\) and \(s=8\times \frac{3\pi}{4}=6\pi\) cm. It is necessary to convert a degree angle into radians first.
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What is the arc length made by an angle of \(60^\circ\) in a circle of radius (10) cm?
A. \( \frac{10\pi}{3} \) सेमी\( \frac{10\pi}{3} \) cm
\(60^\circ=\frac{\pi}{3}\) और \(s=10\times \frac{\pi}{3}=\frac{10\pi}{3}\) सेमी है। चाप लंबाई से पहले कोण को रेडियन में बदलें। / \(60^\circ=\frac{\pi}{3}\) and \(s=10\times \frac{\pi}{3}=\frac{10\pi}{3}\) cm. Convert the angle into radians before finding arc length.
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If (r=12) cm and arc \(s=6\pi\) cm then what is the angle \( \theta \)?
D. \( \frac{\pi}{2} \) रेडियन\( \frac{\pi}{2} \) radians
\( \theta=\frac{s}{r}=\frac{6\pi}{12}=\frac{\pi}{2} \) रेडियन है। \(s=r\theta\) को \( \theta=\frac{s}{r} \) में बदलें। / \( \theta=\frac{s}{r}=\frac{6\pi}{12}=\frac{\pi}{2} \) radians. Rearrange \(s=r\theta\) as \( \theta=\frac{s}{r} \).
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If (r=5) cm and \( \theta=\frac{3\pi}{5} \) radians then what will be the arc length?
C. \(3\pi\) सेमी\(3\pi\) cm
\(s=r\theta=5\times \frac{3\pi}{5}=3\pi\) सेमी है। रेडियन में कोण हो तभी यह सूत्र सीधे लगता है। / \(s=r\theta=5\times \frac{3\pi}{5}=3\pi\) cm. This formula applies directly when the angle is in radians.
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B. (2) रेडियन(2) radians
रेडियन में \( \theta=\frac{s}{r}=\frac{14}{7}=2 \) होता है। चाप लंबाई वाले प्रश्नों में \(s=r\theta\) प्रयोग करें। / In radians \( \theta=\frac{s}{r}=\frac{14}{7}=2 \). Use \(s=r\theta\) in arc length questions.
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Convert (9050'') into degrees minutes seconds.
A. \(2^\circ 30' 50''\)
(9050''=7200''+1850'') और (1850''=30' 50'') है। पहले (3600'') से डिग्री निकालें। / (9050''=7200''+1850'') and (1850''=30' 50''). First find degrees using (3600'').
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How many total seconds are there in \(12^\circ 20' 30''\)?
A. (44430'')
\(12^\circ=43200''\) और (20'=1200'') इसलिए कुल (44430'') है। \(1^\circ=3600''\) याद रखें। / \(12^\circ=43200''\) and (20'=1200'') so the total is (44430''). Remember \(1^\circ=3600''\).
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