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