Level 70 • 46/50 questions • 40 seconds per question.
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If \(\theta=0^\circ\), what is the value of \(\sin \theta\)?
C. (0)
\(\sin 0^\circ=0\) होता है। परीक्षा में मुख्य कोणों के मान याद रखें। / \(\sin 0^\circ=0\). In exams, remember the values of standard angles.
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If \(\theta=0^\circ\), what is the value of \(\cos \theta\)?
A. (1)
\(\cos 0^\circ=1\) होता है। आधारभूत कोणों की सारणी से उत्तर जल्दी मिलता है। / \(\cos 0^\circ=1\). The table of standard angles helps you answer quickly.
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If \(\theta=45^\circ\), what is the value of \(\tan \theta\)?
D. (1)
\(\tan 45^\circ=1\) होता है। \(\tan \theta\) के मुख्य मान अलग से याद रखें। / \(\tan 45^\circ=1\). Learn the standard values of \(\tan \theta\) separately.
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Which trigonometric function is the reciprocal of \(\sin \theta\)?
B. \(\cosec \theta\)
\(\cosec \theta=\frac{1}{\sin \theta}\) होता है। व्युत्क्रम संबंधों को जोड़ों में याद करें। / \(\cosec \theta=\frac{1}{\sin \theta}\). Remember reciprocal relations in pairs.
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Which trigonometric function is the reciprocal of \(\cos \theta\)?
B. \(\sec \theta\)
\(\sec \theta=\frac{1}{\cos \theta}\) होता है। परीक्षा में \(\sec \theta\) और \(\cosec \theta\) को न मिलाएँ। / \(\sec \theta=\frac{1}{\cos \theta}\). Do not confuse \(\sec \theta\) with \(\cosec \theta\) in exams.
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Which trigonometric function is the reciprocal of \(\tan \theta\)?
C. \(\cot \theta\)
\(\cot \theta=\frac{1}{\tan \theta}\) होता है। व्युत्क्रम फलनों को सूत्र रूप में लिखकर जाँचें। / \(\cot \theta=\frac{1}{\tan \theta}\). Check reciprocal functions by writing them as formulas.
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What is \(\tan \theta\) equal to?
A. \(\frac{\sin \theta}{\cos \theta}\)
\(\tan \theta=\frac{\sin \theta}{\cos \theta}\) होता है। भाग वाले संबंध पहचानना आसान प्रश्नों में उपयोगी है। / \(\tan \theta=\frac{\sin \theta}{\cos \theta}\). Recognizing quotient relations is useful in easy questions.
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What is \(\cot \theta\) equal to?
D. \(\frac{\cos \theta}{\sin \theta}\)
\(\cot \theta=\frac{\cos \theta}{\sin \theta}\) होता है। \(\tan \theta\) और \(\cot \theta\) के संबंध उलटे होते हैं। / \(\cot \theta=\frac{\cos \theta}{\sin \theta}\). The relations of \(\tan \theta\) and \(\cot \theta\) are reciprocal.
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What is the value of the basic identity \(\sin^2 \theta+\cos^2 \theta\)?
C. (1)
\(\sin^2 \theta+\cos^2 \theta=1\) मूल सर्वसमिका है। इसे हर अध्याय में आधार सूत्र की तरह प्रयोग करें। / \(\sin^2 \theta+\cos^2 \theta=1\) is a basic identity. Use it as a base formula throughout the chapter.
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What is the value of \(\sec^2 \theta-\tan^2 \theta\)?
D. (1)
\(\sec^2 \theta=1+\tan^2 \theta\) से मान (1) मिलता है। सूत्र को स्थानांतरित करके उत्तर निकालें। / From \(\sec^2 \theta=1+\tan^2 \theta\), the value is (1). Rearrange the formula to get the answer.
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What is the fundamental period of \(\sin \theta\)?
B. \(2\pi\)
\(\sin \theta\) का मूल काल \(2\pi\) होता है। काल संबंधी प्रश्नों में फलन का नाम पहले पहचानें। / The fundamental period of \(\sin \theta\) is \(2\pi\). In period questions, identify the function first.
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What is the fundamental period of \(\cos \theta\)?
D. \(2\pi\)
\(\cos \theta\) का मूल काल \(2\pi\) होता है। \(\sin \theta\) और \(\cos \theta\) का काल समान है। / The fundamental period of \(\cos \theta\) is \(2\pi\). \(\sin \theta\) and \(\cos \theta\) have the same period.
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What is the fundamental period of \(\tan \theta\)?
C. \(\pi\)
\(\tan \theta\) का मूल काल \(\pi\) होता है। \(\tan \theta\) का काल \(\sin \theta\) से अलग है। / The fundamental period of \(\tan \theta\) is \(\pi\). The period of \(\tan \theta\) differs from that of \(\sin \theta\).
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What is the fundamental period of \(\cot \theta\)?
A. \(\pi\)
\(\cot \theta\) का मूल काल \(\pi\) होता है। \(\tan \theta\) और \(\cot \theta\) का काल समान है। / The fundamental period of \(\cot \theta\) is \(\pi\). \(\tan \theta\) and \(\cot \theta\) have the same period.
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What is (\cosec\(-\theta\)) equal to?
B. \(-\cosec \theta\)
\(\cosec \theta\) विषम फलन है इसलिए (\cosec\(-\theta\)=-\cosec \theta)। यह \(\sin \theta\) के व्युत्क्रम जैसा व्यवहार करता है। / \(\cosec \theta\) is an odd function, so (\cosec\(-\theta\)=-\cosec \theta). It behaves like the reciprocal of \(\sin \theta\).
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What is the range of \(\sin \theta\)?
D. ([-1,1])
\(\sin \theta\) का मान हमेशा ([-1,1]) में रहता है। परिसर पूछे जाने पर अधिकतम और न्यूनतम मान देखें। / The value of \(\sin \theta\) always lies in ([-1,1]). For range questions, check the maximum and minimum values.
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Which is the range of \(\cos \theta\)?
A. ([-1,1])
\(\cos \theta\) का परिसर ([-1,1]) है। \(\sin \theta\) और \(\cos \theta\) का परिसर समान होता है। / The range of \(\cos \theta\) is ([-1,1]). \(\sin \theta\) and \(\cos \theta\) have the same range.
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What is the range of \(\tan \theta\)?
C. (\(-\infty,\infty\))
\(\tan \theta\) सभी वास्तविक मान ले सकता है। इसलिए इसका परिसर (\(-\infty,\infty\)) है। / \(\tan \theta\) can take all real values. Therefore its range is (\(-\infty,\infty\)).
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Which is the range of \(\sec \theta\)?
B. (\(-\infty,-1]\cup[1,\infty\))
\(\sec \theta=\frac{1}{\cos \theta}\) होने से इसके मान ([-1,1]) के अंदर नहीं आते। परिसर (\(-\infty,-1]\cup[1,\infty\)) होता है। / Since \(\sec \theta=\frac{1}{\cos \theta}\), its values do not lie inside ([-1,1]). Its range is (\(-\infty,-1]\cup[1,\infty\)).
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What is the range of \(\cosec \theta\)?
D. (\(-\infty,-1]\cup[1,\infty\))
\(\cosec \theta=\frac{1}{\sin \theta}\) होता है। इसका परिसर (\(-\infty,-1]\cup[1,\infty\)) है। / \(\cosec \theta=\frac{1}{\sin \theta}\). Its range is (\(-\infty,-1]\cup[1,\infty\)).
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What is the range of \(\cot \theta\)?
A. (\(-\infty,\infty\))
\(\cot \theta\) सभी वास्तविक मान ले सकता है। \(\tan \theta\) और \(\cot \theta\) का परिसर समान है। / \(\cot \theta\) can take all real values. \(\tan \theta\) and \(\cot \theta\) have the same range.
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When is \(\tan \theta\) undefined?
B. जब \(\cos \theta=0\)when \(\cos \theta=0\)
\(\tan \theta=\frac{\sin \theta}{\cos \theta}\) है इसलिए \(\cos \theta=0\) पर यह अपरिभाषित होता है। हर में शून्य नहीं होना चाहिए। / \(\tan \theta=\frac{\sin \theta}{\cos \theta}\), so it is undefined when \(\cos \theta=0\). The denominator must not be zero.
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When is \(\sec \theta\) undefined?
A. जब \(\cos \theta=0\)when \(\cos \theta=0\)
\(\sec \theta=\frac{1}{\cos \theta}\) है इसलिए \(\cos \theta=0\) पर यह अपरिभाषित है। व्युत्क्रम फलन में हर की जाँच करें। / \(\sec \theta=\frac{1}{\cos \theta}\), so it is undefined when \(\cos \theta=0\). Check the denominator in reciprocal functions.
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When is \(\cosec \theta\) undefined?
C. जब \(\sin \theta=0\)when \(\sin \theta=0\)
\(\cosec \theta=\frac{1}{\sin \theta}\) है इसलिए \(\sin \theta=0\) पर यह अपरिभाषित होता है। हर शून्य होने पर फलन नहीं बनता। / \(\cosec \theta=\frac{1}{\sin \theta}\), so it is undefined when \(\sin \theta=0\). A function is not defined when the denominator is zero.
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When is \(\cot \theta\) undefined?
D. जब \(\sin \theta=0\)when \(\sin \theta=0\)
\(\cot \theta=\frac{\cos \theta}{\sin \theta}\) है इसलिए \(\sin \theta=0\) पर यह अपरिभाषित होता है। भाग वाले फलनों में हर पहचानें। / \(\cot \theta=\frac{\cos \theta}{\sin \theta}\), so it is undefined when \(\sin \theta=0\). In quotient functions, identify the denominator.
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What is (\sin\(\pi+\theta\)) equal to?
A. -\(\sin \theta\)
(\sin\(\pi+\theta\)=-\sin \theta) होता है। तीसरे चतुर्थांश में \(\sin \theta\) का चिह्न ऋण होता है। / (\sin\(\pi+\theta\)=-\sin \theta). In the third quadrant, \(\sin \theta\) is negative.
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What is (\cos\(\pi+\theta\)) equal to?
B. -\(\cos \theta\)
(\cos\(\pi+\theta\)=-\cos \theta) होता है। तीसरे चतुर्थांश में \(\cos \theta\) का चिह्न ऋण होता है। / (\cos\(\pi+\theta\)=-\cos \theta). In the third quadrant, \(\cos \theta\) is negative.
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What is (\tan\(\pi+\theta\)) equal to?
C. \(\tan \theta\)
\(\tan \theta\) का काल \(\pi\) है इसलिए (\tan\(\pi+\theta\)=\tan \theta)। काल याद रखने से रूपांतरण आसान होता है। / The period of \(\tan \theta\) is \(\pi\), so (\tan\(\pi+\theta\)=\tan \theta). Knowing periods makes transformations easier.
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What is (\sin\(2\pi+\theta\)) equal to?
D. \(\sin \theta\)
\(\sin \theta\) का काल \(2\pi\) है इसलिए मान \(\sin \theta\) ही रहता है। पूर्ण चक्र जुड़ने पर \(\sin \theta\) नहीं बदलता। / The period of \(\sin \theta\) is \(2\pi\), so the value remains \(\sin \theta\). Adding a full cycle does not change \(\sin \theta\).
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What is (\cos\(2\pi+\theta\)) equal to?
A. \(\cos \theta\)
\(\cos \theta\) का काल \(2\pi\) है। इसलिए (\cos\(2\pi+\theta\)=\cos \theta) होता है। / The period of \(\cos \theta\) is \(2\pi\). Therefore (\cos\(2\pi+\theta\)=\cos \theta).
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What is (\sin\(\pi-\theta\)) equal to?
B. \(\sin \theta\)
(\sin\(\pi-\theta\)=\sin \theta) होता है। दूसरे चतुर्थांश में \(\sin \theta\) धनात्मक होता है। / (\sin\(\pi-\theta\)=\sin \theta). In the second quadrant, \(\sin \theta\) is positive.
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What is (\cos\(\pi-\theta\)) equal to?
C. -\(\cos \theta\)
(\cos\(\pi-\theta\)=-\cos \theta) होता है। दूसरे चतुर्थांश में \(\cos \theta\) ऋणात्मक होता है। / (\cos\(\pi-\theta\)=-\cos \theta). In the second quadrant, \(\cos \theta\) is negative.
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What is (\tan\(\pi-\theta\)) equal to?
D. -\(\tan \theta\)
(\tan\(\pi-\theta\)=-\tan \theta) होता है। दूसरे चतुर्थांश में \(\tan \theta\) ऋणात्मक होता है। / (\tan\(\pi-\theta\)=-\tan \theta). In the second quadrant, \(\tan \theta\) is negative.
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What is (\sin\left\(\frac{\pi}{2}-\theta\right\)) equal to?
A. \(\cos \theta\)
(\sin\left\(\frac{\pi}{2}-\theta\right\)=\cos \theta) सह-फलन संबंध है। \(\frac{\pi}{2}\) वाले रूपांतरण में फलन बदलता है। / (\sin\left\(\frac{\pi}{2}-\theta\right\)=\cos \theta) is a cofunction relation. In transformations with \(\frac{\pi}{2}\), the function changes.
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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। सह-फलन संबंध में \(\sin \theta\) और \(\cos \theta\) आपस में बदलते हैं। / (\cos\left\(\frac{\pi}{2}-\theta\right\)=\sin \theta). In cofunction relations, \(\sin \theta\) and \(\cos \theta\) interchange.
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What is (\tan\left\(\frac{\pi}{2}-\theta\right\)) equal to?
C. \(\cot \theta\)
(\tan\left\(\frac{\pi}{2}-\theta\right\)=\cot \theta) होता है। \(\tan \theta\) का सह-फलन \(\cot \theta\) है। / (\tan\left\(\frac{\pi}{2}-\theta\right\)=\cot \theta). The cofunction of \(\tan \theta\) is \(\cot \theta\).
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What is (\sec\left\(\frac{\pi}{2}-\theta\right\)) equal to?
D. \(\cosec \theta\)
(\sec\left\(\frac{\pi}{2}-\theta\right\)=\cosec \theta) होता है। \(\sec \theta\) और \(\cosec \theta\) सह-फलन हैं। / (\sec\left\(\frac{\pi}{2}-\theta\right\)=\cosec \theta). \(\sec \theta\) and \(\cosec \theta\) are cofunctions.
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What is the value of \(\sin 30^\circ\)?
A. \(\frac{1}{2}\)
\(\sin 30^\circ=\frac{1}{2}\) होता है। \(30^\circ\) और \(60^\circ\) के मान अक्सर पूछे जाते हैं। / \(\sin 30^\circ=\frac{1}{2}\). Values of \(30^\circ\) and \(60^\circ\) are often asked.
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What is the value of \(\cos 60^\circ\)?
B. \(\frac{1}{2}\)
\(\cos 60^\circ=\frac{1}{2}\) होता है। \(\sin 30^\circ\) और \(\cos 60^\circ\) बराबर होते हैं। / \(\cos 60^\circ=\frac{1}{2}\). \(\sin 30^\circ\) and \(\cos 60^\circ\) are equal.
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What is the value of \(\tan 30^\circ\)?
C. \(\frac{1}{\sqrt{3}}\)
\(\tan 30^\circ=\frac{1}{\sqrt{3}}\) होता है। \(\tan 30^\circ\) और \(\tan 60^\circ\) को अलग-अलग याद करें। / \(\tan 30^\circ=\frac{1}{\sqrt{3}}\). Remember \(\tan 30^\circ\) and \(\tan 60^\circ\) separately.
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What is the value of \(\sin 90^\circ\)?
D. (1)
\(\sin 90^\circ=1\) होता है। मुख्य कोणों की तालिका से यह सीधा मान मिलता है। / \(\sin 90^\circ=1\). This value comes directly from the standard-angle table.
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What is the value of \(\cos 90^\circ\)?
A. (0)
\(\cos 90^\circ=0\) होता है। \(90^\circ\) पर \(\cos \theta\) शून्य हो जाता है। / \(\cos 90^\circ=0\). At \(90^\circ\), \(\cos \theta\) becomes zero.
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What is the value of \(\tan 0^\circ\)?
B. (0)
\(\tan 0^\circ=0\) होता है। \(\tan \theta=\frac{\sin \theta}{\cos \theta}\) से भी इसे जाँचा जा सकता है। / \(\tan 0^\circ=0\). It can also be checked using \(\tan \theta=\frac{\sin \theta}{\cos \theta}\).
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What is the value of \(\sec 0^\circ\)?
C. (1)
\(\sec 0^\circ=\frac{1}{\cos 0^\circ}=1\) होता है। व्युत्क्रम मान निकालते समय मूल फलन का मान पहले लिखें। / \(\sec 0^\circ=\frac{1}{\cos 0^\circ}=1\). While finding reciprocal values, first write the value of the basic function.
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What can \(\sin^2 \theta\) be written as?
A. \(1-\cos^2 \theta\)
\(\sin^2 \theta+\cos^2 \theta=1\) से \(\sin^2 \theta=1-\cos^2 \theta\) मिलता है। परीक्षा में मूल सर्वसमिका को पहले लिखें। / From \(\sin^2 \theta+\cos^2 \theta=1\), we get \(\sin^2 \theta=1-\cos^2 \theta\). In exams, write the basic identity first.
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What is \(\tan^2 \theta+1\) equal to?
B. \(\sec^2 \theta\)
\(\sec^2 \theta=1+\tan^2 \theta\) होता है। \(\tan \theta\) वाले प्रश्नों में \(\sec^2 \theta\) पहचानना उपयोगी है। / \(\sec^2 \theta=1+\tan^2 \theta\). In questions involving \(\tan \theta\), recognizing \(\sec^2 \theta\) is useful.
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