trigonometric-functions se related questions ko ek jagah revise karein. Har question me bilingual content, answer feedback aur explanation available hai.
658 questions tagged with trigonometric-functions.
What is the value of (\tan\(\pi-\theta\))?
B. \(-\tan \theta\)
\(\pi-\theta\) द्वितीय चतुर्थांश में है और tangent ऋणात्मक होता है। परीक्षा में tangent के sign पर विशेष ध्यान दें। / \( \pi-\theta\) is in the second quadrant and tangent is negative. In exams pay special attention to the sign of tangent.
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What is the value of (\cos\(\pi-\theta\))?
A. \(-\cos \theta\)
\(\pi-\theta\) द्वितीय चतुर्थांश में है जहां cosine ऋणात्मक होता है। परीक्षा में चतुर्थांश का चिन्ह जरूर लगाएं। / \( \pi-\theta\) is in the second quadrant where cosine is negative. In exams always apply quadrant sign.
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What is the value of (\sin\(\pi-\theta\))?
C. \(\sin \theta\)
\(\pi-\theta\) द्वितीय चतुर्थांश में आता है और sine धनात्मक रहता है। परीक्षा में allied angle formula याद रखें। / \( \pi-\theta\) lies in the second quadrant and sine remains positive. In exams remember allied angle formulas.
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If (\tan\(-\theta\)=m), then (m) equals what?
B. \(-\tan \theta\)
\(\tan \theta\) विषम फलन है इसलिए (\tan\(-\theta\)=-\tan \theta)। परीक्षा में sign बदलने पर ध्यान दें। / \( \tan \theta\) is an odd function, so ( \tan\(-\theta\)=-\tan \theta). In exams focus on sign change.
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If \(\theta\) is in the second quadrant and \(\cos \theta=-\frac{3}{5}\), what is \(\sin \theta\)?
B. \(\frac{4}{5}\)
\(\sin^2 \theta=1-\cos^2 \theta=\frac{16}{25}\) और द्वितीय चतुर्थांश में \(\sin \theta\) धनात्मक है। परीक्षा में ASTC नियम काम आता है। / \( \sin^2 \theta=1-\cos^2 \theta=\frac{16}{25}\), and \(\sin \theta\) is positive in the second quadrant. In exams ASTC rule helps.
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If \(\theta\) is in the first quadrant and \(\sin \theta=\frac{5}{13}\), what is \(\cos \theta\)?
A. \(\frac{12}{13}\)
\(\cos^2 \theta=1-\sin^2 \theta=\frac{144}{169}\) और प्रथम चतुर्थांश में मान धनात्मक है। परीक्षा में quadrant sign न भूलें। / \( \cos^2 \theta=1-\sin^2 \theta=\frac{144}{169}\), and in the first quadrant it is positive. In exams do not forget quadrant sign.
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What is the simplified value of \(\sec^2 \theta-\tan^2 \theta\)?
A. (1)
\(\sec^2 \theta=1+\tan^2 \theta\) से अंतर (1) मिलता है। परीक्षा में identity को rearrange करें। / From \( \sec^2 \theta=1+\tan^2 \theta\), the difference is (1). In exams rearrange the identity.
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If \(\sin^2 \theta+\cos^2 \theta=k\), what is the value of (k)?
C. (1)
मूल सर्वसमिका \(\sin^2 \theta+\cos^2 \theta=1\) है। परीक्षा में इसे सबसे पहले जांचें। / The basic identity is \( \sin^2 \theta+\cos^2 \theta=1\). In exams check this first.
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If \(\tan \theta=3\), what is the value of \(\frac{\sin \theta}{\cos \theta}\)?
B. (3)
\(\tan \theta=\frac{\sin \theta}{\cos \theta}\) होता है। परीक्षा में परिभाषा सीधे लागू करें। / \( \tan \theta=\frac{\sin \theta}{\cos \theta}\). In exams apply the definition directly.
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B. \(\sin \theta+\cos \theta\)
क्योंकि पूरक कोणों में (\sin\left\(\frac{\pi}{2}-\theta\right\)=\cos \theta) और (\cos\left\(\frac{\pi}{2}-\theta\right\)=\sin \theta) होता है। परीक्षा में co-function सूत्र याद रखें। / Because for complementary angles ( \sin\left\(\frac{\pi}{2}-\theta\right\)=\cos \theta) and ( \cos\left\(\frac{\pi}{2}-\theta\right\)=\sin \theta). In exams remember co-function formulas.
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If \(\tan x=2\), what is the value of \(\frac{\sin x}{\cos x}\)?
A. (2)
\(\tan x=\frac{\sin x}{\cos x}\) होता है। इसलिए दिया गया मान सीधे (2) है। / \(\tan x=\frac{\sin x}{\cos x}\). Therefore, the required value is directly (2).
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What is the range of the function \(\tan x\)?
C. (\(-\infty,\infty\))
\(\tan x\) सभी वास्तविक मान ले सकता है। इसलिए इसका परिसर (\(-\infty,\infty\)) है। / \(\tan x\) can take all real values. Therefore, its range is (\(-\infty,\infty\)).
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What is the range of the function \(\sin x\)?
A. ([-1,1])
\(\sin x\) का मान (-1) से (1) तक होता है। ग्राफ याद रखने से परिसर जल्दी मिलता है। / The value of \(\sin x\) lies from (-1) to (1). Remembering the graph helps find the range quickly.
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What is the period of the function \(\tan x\)?
A. \(\pi\)
\(\tan x\) हर \(\pi\) के बाद अपना मान दोहराता है। \(\tan x\) और \(\cot x\) का काल \(\pi\) होता है। / \(\tan x\) repeats its value after every \(\pi\). The period of \(\tan x\) and \(\cot x\) is \(\pi\).
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Which of the following functions is even?
D. \(\cos x\)
क्योंकि (\cos(-x)=\cos x), इसलिए \(\cos x\) सम फलन है। सम फलन में (f(-x)=f(x)) होता है। / Since (\cos(-x)=\cos x), \(\cos x\) is an even function. For an even function, (f(-x)=f(x)).
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Which of the following functions is odd?
C. \(\sin x\)
क्योंकि (\sin(-x)=-\sin x), इसलिए \(\sin x\) विषम फलन है। विषम फलन में (f(-x)=-f(x)) होता है। / Since (\sin(-x)=-\sin x), \(\sin x\) is an odd function. For an odd function, (f(-x)=-f(x)).
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What is the range of the function \(\cos x\)?
B. ([-1,1])
\(\cos x\) का मान हमेशा (-1) और (1) के बीच रहता है। परिसर में अंतिम मान भी शामिल होते हैं। / The value of \(\cos x\) always lies between (-1) and (1). The end values are included in the range.
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What is the period of the function \(\sin x\)?
C. \(2\pi\)
\(\sin x\) हर \(2\pi\) के बाद अपना मान दोहराता है। परीक्षा में काल पूछने पर सबसे पहले मूल फलन पहचानें। / \(\sin x\) repeats its value after every \(2\pi\). In exams first identify the basic function.
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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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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 \(\frac{\cot \theta}{\cosec \theta}\) 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 \(\frac{\tan \theta}{\sec \theta}\) 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 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 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 \(\sin \theta \cdot \cosec \theta\)?
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 \(\frac{\cos \theta}{\sec \theta}\) 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 \(\frac{\sin \theta}{\cosec \theta}\) 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 \(\cosec^2 \theta-1\) 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 \(\sec^2 \theta-1\) 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 \(\frac{1}{1+\cot^2 \theta}\) 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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