Chapter 6.4, Problem 9E

To determine

To find : an approximate value of ${\cos }^{-1}(-\frac{1}{4})$ correct up to five decimal places.

Answer to Problem 9E

The approximate value of trigonometric expression ${\cos }^{-1}(-\frac{1}{4})$ is $104.47751$ .

Explanation of Solution

Given information:

The given trigonometric expression :

  ${\cos }^{-1}(-\frac{1}{4})$

Formula used:

The given trigonometric expression should be define in its domain.

Calculation:

Consider the given trigonometric function

Recall that the given trigonometric function is defined in its domain

Since the domain of ${\cos }^{-1}(x)$ is $[-1,1]$

Therefore the given function is defined.

So the value of ${\cos }^{-1}(-\frac{1}{4})$ up to five decimal place is $138.59037$ .