angle-transformation se related questions ko ek jagah revise karein. Har question me bilingual content, answer feedback aur explanation available hai.
25 questions tagged with angle-transformation.
What is the correct simplified form of (\cos\(\pi+x\))?
D. \(-\cos x\)
\(\pi+x\) तीसरे चतुर्थांश से जुड़ा रूप है जहाँ \(\cos x\) ऋणात्मक होता है। इसलिए (\cos\(\pi+x\)=-\cos x)। / The form \(\pi+x\) is linked to the third quadrant where \(\cos x\) is negative. Hence (\cos\(\pi+x\)=-\cos x).
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What is \(\sin\left(\frac{\pi}{2}+x\right)\) equal to?
C. \(\cos x\)
\(\frac{\pi}{2}+x\) के लिए sine, cosine में बदलता है और दूसरे चतुर्थांश में धनात्मक रहता है। इसलिए मान \(\cos x\) है। / For \(\frac{\pi}{2}+x\), sine changes to cosine and remains positive in the second quadrant. Hence the value is \(\cos x\).
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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 (\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 \(\tan(2\pi-\theta)\) 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 \(\cos(2\pi-\theta)\) 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 \(\sin(2\pi-\theta)\) 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 \(\cos(\theta-\pi)\) 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 (\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?
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?
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 \(\tan\left(\frac{3\pi}{2}+\theta\right)\) 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 \(\cos\left(\frac{3\pi}{2}+\theta\right)\) 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 \(\sin\left(\frac{3\pi}{2}+\theta\right)\) 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 \(\tan\left(\frac{3\pi}{2}-\theta\right)\) 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 \(\cos\left(\frac{3\pi}{2}-\theta\right)\) 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 \(\sin\left(\frac{3\pi}{2}-\theta\right)\) 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 \(\cos\left(\frac{\pi}{2}+\theta\right)\) 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 \(\sin\left(\frac{\pi}{2}+\theta\right)\) 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 \(\tan(\pi-\theta)\) 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 \(\cos(\pi-\theta)\) 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 \(\sin(\pi-\theta)\) 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 (\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 \(\cos(\pi+\theta)\) 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 \(\sin(\pi+\theta)\) 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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