Question

In Problems 13–24, find the exact value of each expression.

sin^-1 0

Short answer

The exact value of sin^-1 0 is 0.

Step-by-step solution

Step 1. Given Information:

Given expression: sin^-1 0

We want to find the exact value of each expression.

Step 2. Solution:

The given expression can be rewritten as:

${\sin }^{-1}0=y;-\frac{\mathrm{\pi }}{2}\le y\le \frac{\mathrm{\pi }}{2}$

Hence we get sin (y) = 0

Since we have sin^-1 function initially, the bounds on the sin function are going to be in the interval $[-\frac{\mathrm{\pi }}{2},\frac{\mathrm{\pi }}{2}]$which represents the range of sin^-1 function.

Using the unit circle, we know that in order to get 0, y must be equal to 0.

Hence, we get sin^-10 = 0