Question

$1)$ Principal value of $\cos \theta =-1$ is $\pi$
$2)$ Principal value of $\sin \theta =0$ is $\pi$
Which of the above statement is correct?

• A. Only I
• B. Only II
• C. Both I and II
• D. Neither I or II

Answer 1

Answer: (A)

Only I

we know that ,

$\cos \theta =-1\Rightarrow \theta ={\cos }^{-1}(-1)\Rightarrow \theta =\pi$

as Range of Principal Value of ${\cos }^{-1}$ is $[0,\pi ]$

But, $\sin \theta =0\Rightarrow \theta ={\sin }^{-1}\left(0\right)\Rightarrow \theta =0$

as Range of Principal Value of ${\sin }^{-1}$ is $[\frac{-\pi }{2},\frac{\pi }{2}]$

Therefore, Only, $\left(1\right)$ is Correct