Chapter SH, Problem 12.17EP

To determine

To find: The exact value of given value.

Answer to Problem 12.17EP

The value of the function $\cos \left(-\frac{3\pi }{4}\right)$ is $-\frac{1}{\sqrt{2}}$ .

Explanation of Solution

Given:

The given function is:

  $\cos \left(-\frac{3\pi }{4}\right)$

The value of given function is calculated as:

  $\begin{array}{c}\sin \left(-\frac{3\pi }{4}\right)=-\sin \left(\frac{3\pi }{4}\right)\left[\because \sin \left(-\theta \right)=-\sin \theta \right]\\ =-\sin \left(\pi -\frac{\pi }{4}\right)\\ =-\left(\sin \frac{\pi }{4}\right)\left[\because \sin \left(\pi -\theta \right)=\sin \theta \right]\\ =-\frac{1}{\sqrt{2}}\end{array}$

Therefore the value of the function $\cos \left(-\frac{3\pi }{4}\right)$ is $-\frac{1}{\sqrt{2}}$ .