Question

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

cos^-1 (- 1)

Short answer

The exact value of cos^-1 (- 1) is$\mathrm{\pi }$.

Step-by-step solution

Step 1. Given Information: 

Given expression: cos^-1 (- 1)

We want to find the exact value of given expression.

Step 2. Solution: 

The given expression can be rewritten as:

${\cos }^{-1}(-1)=x;0\le x\le \mathrm{\pi }$

Hence we get cos (x) = - 1

Since we have cos^-1 function initially, the bounds on the cos function are going to be in the interval $[0,\mathrm{\pi }]$ which represents the range of cos^-1 function.

Using the unit circle, we know that in order to get (- 1), x must be equal to $\mathrm{\pi }$.

Hence, we get ${\cos }^{-1}(-1)=\mathrm{\pi }$