Question

Find all possible values for each expression. sin^-1 1/2 a. 30° + 180n, 150° + 180n b. 30° + 360n, 150° + 360n c. 60° + 180n, 120° + 180n d. 60° + 360n, 120° + 360n

Answer 1

Answer:

Option B.

Step-by-step explanation:

The given expression is

$\sin^{-1}\left(\dfrac{1}{2}\right)$

It can be written as

$\sin^{-1}\left(\dfrac{1}{2}\right)=\sin^{-1}\left(\sin (30^\circ\right)$    $[\because \sin (30^\circ)=\dfrac{1}{2}]$

$\sin^{-1}\left(\dfrac{1}{2}\right)=30^\circ$

We know that sin is positive in first and second quadrant.

For first quadrant,

$\theta=30^\circ$

For second quadrant,

$\pi-\theta =180-30=150^\circ$

So, the required angles are $30^\circ+360n,150^\circ+360n$.

Therefore, the correct option is B.