Chapter 7: Q. 19 (page 450)

In Problems 13–24, find the exact value of each expression.
$\sin^{- 1} \frac{\sqrt{2}}{2}$

Short Answer

Expert verified

The exact value of $\sin^{- 1} \frac{\sqrt{2}}{2} i s \frac{π}{4}$ .

Step by step solution

Step 1. Given Information:

Given expression: $\sin^{- 1} \frac{\sqrt{2}}{2}$

We want to find the exact value of given expression.

Step 2. Solution:

The given expression can be rewritten as:

$\sin^{- 1} \frac{\sqrt{2}}{2} = y; - \frac{π}{2} \leq y \leq \frac{π}{2}$

Hence we get $\sin y = \frac{\sqrt{2}}{2}$

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

Using the unit circle, we know that in order to get $\frac{\sqrt{2}}{2}$ , y must be equal to $\frac{π}{4}$ .

Hence, we get $\sin^{- 1} \frac{\sqrt{2}}{2} = \frac{π}{4}$ .

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In Problems 13–24, find the exact value of each expression.
$\sin^{- 1} \frac{\sqrt{2}}{2}$

Short Answer

Step by step solution

Step 1. Given Information:

Step 2. Solution:

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Short Answer

Step by step solution

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In Problems 13–24, find the exact value of each expression.
$\sin^{- 1} \frac{\sqrt{2}}{2}$