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Chapter 7: Q. 15 (page 450)

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

sin-1 (- 1)

Short Answer

Expert verified

The exact value of sin-1 (- 1) is-蟺2.

Step by step solution

01

Step 1. Given Information:

Given expression: sin-1 (- 1)

We want to find the exact value of given expression.

02

Step 2. Solution:

The given expression can be rewritten as:

sin-1(-1)=y;-蟺2鈮�y鈮�蟺2

Hence we get sin (y) = - 1

Since we have sin-1 function initially, the bounds on the sin function are going to be in the interval localid="1647536843358" -蟺2,蟺2 which represents the range of sin-1 function.

Using the unit circle, we know that in order to get (- 1), y must be equal to -蟺2.

Hence, we getlocalid="1647536511185" sin-1(-1)=-蟺2

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