Chapter 12.6, Problem 4AGP

To determine

To find the exact value of $\cos \left(-\frac{3\pi }{4}\right)$ .

Answer to Problem 4AGP

  $-\frac{1}{\sqrt{2}}$

Explanation of Solution

Given:

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

Formula used:

  $\cos \left(-\theta \right)=\cos \left(\theta \right)$

Calculation:

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

Here, the angle $\frac{3\pi }{4}$ lies in second quadrant, where the $\cos$ ratio has a negative value.

Now the related acute angle for $\frac{3\pi }{4}$ is $\frac{\pi }{4}$ .

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

  $=-\frac{1}{\sqrt{2}}$

Conclusion:

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