Question

If $\sin \theta=\frac{12}{13}, \cos \theta=-\frac{5}{13}, 0<\theta<2 \pi$. Consider the following statements.
I. $\theta=\cos ^{-1}\left(-\frac{5}{13}\right)$
II. $\theta=\sin ^{-1}\left(\frac{12}{13}\right)$
III. $\theta=\pi-\sin ^{-1}\left(\frac{12}{13}\right)$
IV. $\theta=\tan ^{-1}\left(-\frac{12}{5}\right)$
V. $\theta=\pi-\tan ^{-1}\left(\frac{12}{5}\right)$
then which of the following statements are true?

• A. I, II and IV only
• B. III and V only
• C. I and III only
• D. I, III and V only

Answer 1

Answer: (D)

$\theta$ must line in the $2^{\text {nd }}$ quadrant