Level 71 • 50/50 questions • 40 seconds per question.
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What is the sign of \(\sin \theta\) in the first quadrant?
A. धनात्मकPositive
पहले चतुर्थांश में सभी त्रिकोणमितीय फलन धनात्मक होते हैं। परीक्षा में चतुर्थांश के चिह्न याद रखें। / In the first quadrant, all trigonometric functions are positive. Remember quadrant signs for exams.
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Which function is positive in the second quadrant?
B. \(\sin \theta\)
दूसरे चतुर्थांश में \(\sin \theta\) और \(\cosec \theta\) धनात्मक होते हैं। चिह्न नियम को याद रखने से ऐसे प्रश्न जल्दी हल होते हैं। / In the second quadrant, \(\sin \theta\) and \(\cosec \theta\) are positive. Knowing sign rules helps solve such questions quickly.
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What is the sign of \(\tan \theta\) in the third quadrant?
C. धनात्मकPositive
तीसरे चतुर्थांश में \(\tan \theta\) और \(\cot \theta\) धनात्मक होते हैं। चतुर्थांश के अनुसार चिह्न बदलता है। / In the third quadrant, \(\tan \theta\) and \(\cot \theta\) are positive. The sign changes according to the quadrant.
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Which function is positive in the fourth quadrant?
D. \(\cos \theta\)
चौथे चतुर्थांश में \(\cos \theta\) और \(\sec \theta\) धनात्मक होते हैं। संकेत नियम को छोटी तालिका से याद करें। / In the fourth quadrant, \(\cos \theta\) and \(\sec \theta\) are positive. Remember sign rules using a small table.
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What is (\sin\left\(\frac{\pi}{2}+\theta\right\)) equal to?
A. \(\cos \theta\)
\(\frac{\pi}{2}\) के साथ \(\sin \theta\) सह-फलन \(\cos \theta\) में बदलता है। दूसरे चतुर्थांश में चिह्न धनात्मक रहता है। / With \(\frac{\pi}{2}\), \(\sin \theta\) changes to its cofunction \(\cos \theta\). The sign remains positive in the second quadrant.
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What is (\cos\left\(\frac{\pi}{2}+\theta\right\)) equal to?
B. -\(\sin \theta\)
(\cos\left\(\frac{\pi}{2}+\theta\right\)=-\sin \theta) होता है। \(\frac{\pi}{2}\) पर फलन बदलता है और चिह्न चतुर्थांश से तय होता है। / (\cos\left\(\frac{\pi}{2}+\theta\right\)=-\sin \theta). At \(\frac{\pi}{2}\), the function changes and the sign is decided by the quadrant.
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What is (\tan\left\(\frac{\pi}{2}+\theta\right\)) equal to?
C. -\(\cot \theta\)
\(\tan \theta\) का सह-फलन \(\cot \theta\) है और दूसरे चतुर्थांश में चिह्न ऋणात्मक होता है। इसलिए उत्तर \(-\cot \theta\) है। / The cofunction of \(\tan \theta\) is \(\cot \theta\), and the sign is negative in the second quadrant. Therefore the answer is \(-\cot \theta\).
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What is (\cot\left\(\frac{\pi}{2}+\theta\right\)) equal to?
D. -\(\tan \theta\)
\(\cot \theta\) का सह-फलन \(\tan \theta\) है और दूसरे चतुर्थांश में चिह्न ऋणात्मक होता है। ऐसे प्रश्नों में पहले सह-फलन पहचानें। / The cofunction of \(\cot \theta\) is \(\tan \theta\), and the sign is negative in the second quadrant. In such questions, first identify the cofunction.
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What is (\sec\left\(\frac{\pi}{2}+\theta\right\)) equal to?
A. -\(\cosec \theta\)
\(\sec \theta\) का सह-फलन \(\cosec \theta\) है और दूसरे चतुर्थांश में \(\sec \theta\) ऋणात्मक होता है। इसलिए मान \(-\cosec \theta\) है। / The cofunction of \(\sec \theta\) is \(\cosec \theta\), and \(\sec \theta\) is negative in the second quadrant. Hence the value is \(-\cosec \theta\).
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What is (\cosec\left\(\frac{\pi}{2}+\theta\right\)) equal to?
B. \(\sec \theta\)
\(\cosec \theta\) का सह-फलन \(\sec \theta\) है और दूसरे चतुर्थांश में चिह्न धनात्मक रहता है। सह-फलन जोड़ों को याद रखें। / The cofunction of \(\cosec \theta\) is \(\sec \theta\), and the sign remains positive in the second quadrant. Remember cofunction pairs.
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What is (\sin\left\(\frac{3\pi}{2}-\theta\right\)) equal to?
C. -\(\cos \theta\)
\(\frac{3\pi}{2}\) के साथ \(\sin \theta\) सह-फलन में बदलता है और तीसरे चतुर्थांश में चिह्न ऋणात्मक होता है। इसलिए उत्तर \(-\cos \theta\) है। / With \(\frac{3\pi}{2}\), \(\sin \theta\) changes to a cofunction and the sign is negative in the third quadrant. So the answer is \(-\cos \theta\).
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What is (\cos\left\(\frac{3\pi}{2}-\theta\right\)) equal to?
A. -\(\sin \theta\)
\(\frac{3\pi}{2}\) के साथ \(\cos \theta\) सह-फलन \(\sin \theta\) में बदलता है। तीसरे चतुर्थांश में \(\cos \theta\) ऋणात्मक होता है। / With \(\frac{3\pi}{2}\), \(\cos \theta\) changes to the cofunction \(\sin \theta\). In the third quadrant, \(\cos \theta\) is negative.
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What is (\tan\left\(\frac{3\pi}{2}-\theta\right\)) equal to?
B. \(\cot \theta\)
\(\frac{3\pi}{2}\) के साथ \(\tan \theta\) \(\cot \theta\) में बदलता है। तीसरे चतुर्थांश में \(\tan \theta\) धनात्मक होता है। / With \(\frac{3\pi}{2}\), \(\tan \theta\) changes to \(\cot \theta\). In the third quadrant, \(\tan \theta\) is positive.
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What is (\sin\left\(\frac{3\pi}{2}+\theta\right\)) equal to?
C. -\(\cos \theta\)
(\sin\left\(\frac{3\pi}{2}+\theta\right\)=-\cos \theta) होता है। \(\frac{3\pi}{2}\) वाले रूप में \(\sin \theta\) सह-फलन में बदलता है। / (\sin\left\(\frac{3\pi}{2}+\theta\right\)=-\cos \theta). In a \(\frac{3\pi}{2}\) form, \(\sin \theta\) changes to its cofunction.
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What is (\cos\left\(\frac{3\pi}{2}+\theta\right\)) equal to?
D. \(\sin \theta\)
(\cos\left\(\frac{3\pi}{2}+\theta\right\)=\sin \theta) होता है। चौथे चतुर्थांश में \(\cos \theta\) धनात्मक माना जाता है। / (\cos\left\(\frac{3\pi}{2}+\theta\right\)=\sin \theta). In the fourth quadrant, \(\cos \theta\) is taken as positive.
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What is (\tan\left\(\frac{3\pi}{2}+\theta\right\)) equal to?
A. -\(\cot \theta\)
\(\frac{3\pi}{2}\) के साथ \(\tan \theta\) \(\cot \theta\) में बदलता है और चौथे चतुर्थांश में चिह्न ऋणात्मक होता है। इसलिए उत्तर \(-\cot \theta\) है। / With \(\frac{3\pi}{2}\), \(\tan \theta\) changes to \(\cot \theta\), and the sign is negative in the fourth quadrant. Therefore the answer is \(-\cot \theta\).
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What is (\sin\(\theta+2\pi\)) equal to?
B. \(\sin \theta\)
\(\sin \theta\) का काल \(2\pi\) है इसलिए \(2\pi\) जोड़ने से मान नहीं बदलता। काल का उपयोग करके बड़े कोण सरल करें। / The period of \(\sin \theta\) is \(2\pi\), so adding \(2\pi\) does not change its value. Use periods to simplify large angles.
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What is (\cos\(\theta+2\pi\)) equal to?
C. \(\cos \theta\)
\(\cos \theta\) का काल \(2\pi\) होता है। इसलिए (\cos\(\theta+2\pi\)=\cos \theta) है। / The period of \(\cos \theta\) is \(2\pi\). Therefore (\cos\(\theta+2\pi\)=\cos \theta).
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What is (\tan\(\theta+\pi\)) equal to?
D. \(\tan \theta\)
\(\tan \theta\) का काल \(\pi\) है इसलिए (\tan\(\theta+\pi\)=\tan \theta)। \(\tan \theta\) के लिए \(2\pi\) की जरूरत नहीं होती। / The period of \(\tan \theta\) is \(\pi\), so (\tan\(\theta+\pi\)=\tan \theta). For \(\tan \theta\), \(2\pi\) is not needed.
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What is (\cot\(\theta+\pi\)) equal to?
A. \(\cot \theta\)
\(\cot \theta\) का काल \(\pi\) होता है। इसलिए (\cot\(\theta+\pi\)) का मान \(\cot \theta\) ही रहता है। / The period of \(\cot \theta\) is \(\pi\). Therefore (\cot\(\theta+\pi\)) remains \(\cot \theta\).
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What is (\sec\(\theta+2\pi\)) equal to?
B. \(\sec \theta\)
\(\sec \theta\) का काल \(2\pi\) है क्योंकि यह \(\cos \theta\) का व्युत्क्रम है। इसलिए \(2\pi\) जोड़ने पर मान वही रहता है। / The period of \(\sec \theta\) is \(2\pi\) because it is the reciprocal of \(\cos \theta\). Hence adding \(2\pi\) keeps the value same.
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What is (\cosec\(\theta+2\pi\)) equal to?
C. \(\cosec \theta\)
\(\cosec \theta\) का काल \(2\pi\) है क्योंकि यह \(\sin \theta\) का व्युत्क्रम है। काल से उत्तर तुरंत मिलता है। / The period of \(\cosec \theta\) is \(2\pi\) because it is the reciprocal of \(\sin \theta\). The period gives the answer directly.
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What is (\sin\(\theta+\pi\)) equal to?
D. -\(\sin \theta\)
(\sin\(\theta+\pi\)=-\sin \theta) होता है। \(\pi\) जोड़ने पर \(\sin \theta\) का चिह्न बदल जाता है। / (\sin\(\theta+\pi\)=-\sin \theta). Adding \(\pi\) changes the sign of \(\sin \theta\).
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What is (\cos\(\theta+\pi\)) equal to?
A. -\(\cos \theta\)
(\cos\(\theta+\pi\)=-\cos \theta) होता है। आधा चक्र जोड़ने से \(\cos \theta\) का चिह्न बदलता है। / (\cos\(\theta+\pi\)=-\cos \theta). Adding half a cycle changes the sign of \(\cos \theta\).
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What is (\sin\(\theta-\pi\)) equal to?
B. -\(\sin \theta\)
(\sin\(\theta-\pi\)=-\sin \theta) होता है। \(\pi\) घटाने पर भी \(\sin \theta\) का चिह्न बदलता है। / (\sin\(\theta-\pi\)=-\sin \theta). Subtracting \(\pi\) also changes the sign of \(\sin \theta\).
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What is (\cos\(\theta-\pi\)) equal to?
C. -\(\cos \theta\)
(\cos\(\theta-\pi\)=-\cos \theta) होता है। \(\pi\) का अंतर \(\cos \theta\) का चिह्न बदल देता है। / (\cos\(\theta-\pi\)=-\cos \theta). A difference of \(\pi\) changes the sign of \(\cos \theta\).
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What is (\tan\(\theta-\pi\)) equal to?
D. \(\tan \theta\)
\(\tan \theta\) का काल \(\pi\) है इसलिए (\tan\(\theta-\pi\)=\tan \theta)। काल घटाने पर भी मान वही रहता है। / The period of \(\tan \theta\) is \(\pi\), so (\tan\(\theta-\pi\)=\tan \theta). Subtracting the period keeps the value same.
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What is (\sin\(2\pi-\theta\)) equal to?
A. -\(\sin \theta\)
(\sin\(2\pi-\theta\)=-\sin \theta) होता है। चौथे चतुर्थांश में \(\sin \theta\) ऋणात्मक होता है। / (\sin\(2\pi-\theta\)=-\sin \theta). In the fourth quadrant, \(\sin \theta\) is negative.
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What is (\cos\(2\pi-\theta\)) equal to?
B. \(\cos \theta\)
(\cos\(2\pi-\theta\)=\cos \theta) होता है। चौथे चतुर्थांश में \(\cos \theta\) धनात्मक होता है। / (\cos\(2\pi-\theta\)=\cos \theta). In the fourth quadrant, \(\cos \theta\) is positive.
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What is (\tan\(2\pi-\theta\)) equal to?
C. -\(\tan \theta\)
(\tan\(2\pi-\theta\)=-\tan \theta) होता है। चौथे चतुर्थांश में \(\tan \theta\) ऋणात्मक होता है। / (\tan\(2\pi-\theta\)=-\tan \theta). In the fourth quadrant, \(\tan \theta\) is negative.
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What is (\sec\(2\pi-\theta\)) equal to?
D. \(\sec \theta\)
\(\sec \theta\) \(\cos \theta\) का व्युत्क्रम है और चौथे चतुर्थांश में धनात्मक रहता है। इसलिए (\sec\(2\pi-\theta\)=\sec \theta) है। / \(\sec \theta\) is the reciprocal of \(\cos \theta\) and remains positive in the fourth quadrant. So (\sec\(2\pi-\theta\)=\sec \theta).
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What is (\cosec\(2\pi-\theta\)) equal to?
A. -\(\cosec \theta\)
\(\cosec \theta\) \(\sin \theta\) का व्युत्क्रम है और चौथे चतुर्थांश में ऋणात्मक होता है। इसलिए मान \(-\cosec \theta\) है। / \(\cosec \theta\) is the reciprocal of \(\sin \theta\) and is negative in the fourth quadrant. Therefore the value is \(-\cosec \theta\).
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What is the maximum value of \(\sin^2 \theta\)?
B. (1)
\(\sin \theta\) का मान ([-1,1]) में होता है इसलिए \(\sin^2 \theta\) का अधिकतम मान (1) है। वर्ग करने पर मान ऋणात्मक नहीं रहता। / The value of \(\sin \theta\) lies in ([-1,1]), so the maximum value of \(\sin^2 \theta\) is (1). Squaring makes the value non-negative.
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What is the minimum value of \(\cos^2 \theta\)?
C. (0)
\(\cos^2 \theta\) हमेशा (0) या धनात्मक होता है। इसका न्यूनतम मान (0) है। / \(\cos^2 \theta\) is always (0) or positive. Its minimum value is (0).
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What type of value does \(\sin^2 \theta+\cos^2 \theta\) have?
D. स्थिरConstant
\(\sin^2 \theta+\cos^2 \theta=1\) होता है इसलिए यह स्थिर मान है। मूल सर्वसमिका सीधे पहचानें। / \(\sin^2 \theta+\cos^2 \theta=1\), so it is a constant value. Identify the basic identity directly.
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If \(\sin \theta=0\), what is the value of \(\cos^2 \theta\)?
A. (1)
\(\sin^2 \theta+\cos^2 \theta=1\) में \(\sin \theta=0\) रखने पर \(\cos^2 \theta=1\) मिलता है। ऐसे प्रश्नों में पहचान सूत्र लगाएँ। / Putting \(\sin \theta=0\) in \(\sin^2 \theta+\cos^2 \theta=1\) gives \(\cos^2 \theta=1\). Use the identity in such questions.
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If \(\cos \theta=0\), what is the value of \(\sin^2 \theta\)?
B. (1)
\(\sin^2 \theta+\cos^2 \theta=1\) में \(\cos \theta=0\) रखने पर \(\sin^2 \theta=1\) आता है। ज्ञात मान को सूत्र में रखें। / Putting \(\cos \theta=0\) in \(\sin^2 \theta+\cos^2 \theta=1\) gives \(\sin^2 \theta=1\). Substitute the known value in the formula.
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What is \(\frac{1}{1+\tan^2 \theta}\) equal to?
C. \(\cos^2 \theta\)
\(\1+\tan^2 \theta=\sec^2 \theta\) और \(\frac{1}{\sec^2 \theta}=\cos^2 \theta\) होता है। व्युत्क्रम लेते समय सावधानी रखें। / \(\1+\tan^2 \theta=\sec^2 \theta\) and \(\frac{1}{\sec^2 \theta}=\cos^2 \theta\). Be careful while taking reciprocals.
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What is \(\frac{1}{1+\cot^2 \theta}\) equal to?
D. \(\sin^2 \theta\)
\(\1+\cot^2 \theta=\cosec^2 \theta\) और \(\frac{1}{\cosec^2 \theta}=\sin^2 \theta\) होता है। पहचान सूत्र से भिन्न सरल करें। / \(\1+\cot^2 \theta=\cosec^2 \theta\) and \(\frac{1}{\cosec^2 \theta}=\sin^2 \theta\). Simplify fractions using identities.
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What is \(\sec^2 \theta-1\) equal to?
A. \(\tan^2 \theta\)
\(\sec^2 \theta=1+\tan^2 \theta\) से \(\sec^2 \theta-1=\tan^2 \theta\) मिलता है। सूत्र को सरल रूप में बदलें। / From \(\sec^2 \theta=1+\tan^2 \theta\), we get \(\sec^2 \theta-1=\tan^2 \theta\). Rearrange the formula into a simple form.
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What is \(\cosec^2 \theta-1\) equal to?
B. \(\cot^2 \theta\)
\(\cosec^2 \theta=1+\cot^2 \theta\) से \(\cosec^2 \theta-1=\cot^2 \theta\) होता है। समान पहचान सूत्रों की जोड़ी बनाकर अभ्यास करें। / From \(\cosec^2 \theta=1+\cot^2 \theta\), \(\cosec^2 \theta-1=\cot^2 \theta\). Practice similar identities in pairs.
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What is \(\frac{\sin \theta}{\cosec \theta}\) equal to?
C. \(\sin^2 \theta\)
\(\cosec \theta=\frac{1}{\sin \theta}\) इसलिए \(\frac{\sin \theta}{\cosec \theta}=\sin^2 \theta\) है। व्युत्क्रम संबंध को भिन्न में बदलें। / Since \(\cosec \theta=\frac{1}{\sin \theta}\), \(\frac{\sin \theta}{\cosec \theta}=\sin^2 \theta\). Convert reciprocal relations into fractions.
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What is \(\frac{\cos \theta}{\sec \theta}\) equal to?
D. \(\cos^2 \theta\)
\(\sec \theta=\frac{1}{\cos \theta}\) इसलिए \(\frac{\cos \theta}{\sec \theta}=\cos^2 \theta\) होता है। व्युत्क्रम लिखने से सरलीकरण आसान होता है। / Since \(\sec \theta=\frac{1}{\cos \theta}\), \(\frac{\cos \theta}{\sec \theta}=\cos^2 \theta\). Writing the reciprocal makes simplification easy.
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What is the value of \(\sin \theta \cdot \cosec \theta\)?
A. (1)
\(\sin \theta\) और \(\cosec \theta\) परस्पर व्युत्क्रम हैं इसलिए उनका गुणनफल (1) होता है। व्युत्क्रम जोड़ों को याद रखें। / \(\sin \theta\) and \(\cosec \theta\) are reciprocals, so their product is (1). Remember reciprocal pairs.
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What is the value of \(\cos \theta \cdot \sec \theta\)?
B. (1)
\(\cos \theta\) और \(\sec \theta\) एक-दूसरे के व्युत्क्रम हैं। इसलिए उनका गुणनफल (1) है। / \(\cos \theta\) and \(\sec \theta\) are reciprocals of each other. Therefore their product is (1).
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What is the value of \(\tan \theta \cdot \cot \theta\)?
C. (1)
\(\tan \theta\) और \(\cot \theta\) परस्पर व्युत्क्रम हैं। इसलिए गुणनफल (1) होता है। / \(\tan \theta\) and \(\cot \theta\) are reciprocals. Hence their product is (1).
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What is \(\frac{\tan \theta}{\sec \theta}\) equal to?
D. \(\sin \theta\)
\(\tan \theta=\frac{\sin \theta}{\cos \theta}\) और \(\sec \theta=\frac{1}{\cos \theta}\) रखने पर उत्तर \(\sin \theta\) मिलता है। भाग को भिन्न में बदलकर काटें। / Using \(\tan \theta=\frac{\sin \theta}{\cos \theta}\) and \(\sec \theta=\frac{1}{\cos \theta}\), the answer is \(\sin \theta\). Convert division into fractions and cancel.
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What is \(\frac{\cot \theta}{\cosec \theta}\) equal to?
A. \(\cos \theta\)
\(\cot \theta=\frac{\cos \theta}{\sin \theta}\) और \(\cosec \theta=\frac{1}{\sin \theta}\) रखने पर \(\cos \theta\) मिलता है। मानक रूप लिखना सबसे सुरक्षित तरीका है। / Using \(\cot \theta=\frac{\cos \theta}{\sin \theta}\) and \(\cosec \theta=\frac{1}{\sin \theta}\), we get \(\cos \theta\). Writing standard forms is the safest method.
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What is \(\frac{\sec \theta}{\tan \theta}\) equal to?
B. \(\cosec \theta\)
\(\sec \theta=\frac{1}{\cos \theta}\) और \(\tan \theta=\frac{\sin \theta}{\cos \theta}\) से \(\frac{1}{\sin \theta}=\cosec \theta\) मिलता है। भिन्नों को सावधानी से सरल करें। / From \(\sec \theta=\frac{1}{\cos \theta}\) and \(\tan \theta=\frac{\sin \theta}{\cos \theta}\), we get \(\frac{1}{\sin \theta}=\cosec \theta\). Simplify fractions carefully.
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What is \(\frac{\cosec \theta}{\cot \theta}\) equal to?
A. \(\sec \theta\)
\(\cosec \theta=\frac{1}{\sin \theta}\) और \(\cot \theta=\frac{\cos \theta}{\sin \theta}\) से \(\frac{1}{\cos \theta}=\sec \theta\) मिलता है। अंतिम उत्तर को मानक फलन में लिखें। / From \(\cosec \theta=\frac{1}{\sin \theta}\) and \(\cot \theta=\frac{\cos \theta}{\sin \theta}\), we get \(\frac{1}{\cos \theta}=\sec \theta\). Write the final answer as a standard function.
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