Chapter 7, Problem 91RE

To determine

To find:the exact value of the given expression.

Answer to Problem 91RE

  ${\cos }^{-1}\left({\sin }^{-1}\frac{3}{5}-{\cos }^{-1}\frac{1}{2}\right)=1.98$ .

Explanation of Solution

Given:

The givenexpression is ${\cos }^{-1}\left({\sin }^{-1}\frac{3}{5}-{\cos }^{-1}\frac{1}{2}\right)$ .

Calculation:

As the given expression is ${\cos }^{-1}\left({\sin }^{-1}\frac{3}{5}-{\cos }^{-1}\frac{1}{2}\right)$ .

Now, the value of thegiven expression is

  $\begin{array}{l}{\cos }^{-1}\left({\sin }^{-1}\frac{3}{5}-{\cos }^{-1}\frac{1}{2}\right)\\ \left\{\text{substitute the vaslue of }{\sin }^{-1}\frac{3}{5}=0.6435,{\cos }^{-1}\frac{1}{2}=\frac{\pi }{3}=1.0471\right\}\\ ={\cos }^{-1}\left(0.6435-1.0471\right)\\ ={\cos }^{-1}0.4036\\ =1.9862\end{array}$

Hence, the exact value of the given expression ${\cos }^{-1}\left({\sin }^{-1}\frac{3}{5}-{\cos }^{-1}\frac{1}{2}\right)=1.98$ .