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

Option B.

Explanation:

The given expression is

`\sin^(-1)\left((1)/(2)\right)`

It can be written as

`\sin^(-1)\left((1)/(2)\right)=\sin^(-1)\left(\sin (30^\circ\right)`
`[\because \sin (30^\circ)=(1)/(2)]`

`\sin^(-1)\left((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.