Chapter 6.4, Problem 11E

To determine

To find: an approximate value of ${\tan }^{-1}(3)$ correct up to five decimal places.

Answer to Problem 11E

The approximate value of trigonometric expression ${\tan }^{-1}(3)$ is $71.56505$ .

Explanation of Solution

Given information:

The given trigonometric expression :

  ${\tan }^{-1}(3)$

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 define in its domain

Since the domain of ${\tan }^{-1}(x)$ is $(-\infty ,\infty )$

Therefore the given function is defined.

So the value of ${\tan }^{-1}(3)$ up to five decimal place is $71.56505$ .