Chapter 14.7, Problem 11WE

To determine

To Find: The value of the given trigonometric equation.

Answer to Problem 11WE

The value of the expression is $\frac{-3}{4}$ .

Explanation of Solution

Given:

The given expression is $\tan \left[{\sin }^{-1}\left(\frac{-3}{5}\right)\right]$ .

Calculation:

Consider the given trigonometric expression is,

  $\tan \left[{\sin }^{-1}\left(\frac{-3}{5}\right)\right]$

Let us take $y={\sin }^{-1}\left(\frac{-3}{5}\right)$ then,

  $\sin y=\left(\frac{-3}{5}\right)$

Then, the value of $\cos y$ is obtained as,

  $\begin{array}{c}\cos y=\sqrt{1-{\left(\frac{-3}{5}\right)}^2}\\ =\frac{4}{5}\end{array}$

Then, the given expression is,

  $\begin{array}{c}\tan y=\tan \left[{\sin }^{-1}\left(\frac{-3}{5}\right)\right]\\ =\frac{\sin y}{\cos y}\\ =\frac{\frac{-3}{5}}{\frac{4}{4}}\\ =\frac{-3}{4}\end{array}$