Question

use reference angles to find the exact value. rationalize the denominator of your answer, if needed. select \undefined\ if applicable. $cos\frac{3pi}{4}=$

Explanation:

Step1: Determine the quadrant

The angle $\frac{3\pi}{4}$ is in the second - quadrant ($\frac{\pi}{2}<\frac{3\pi}{4}<\pi$).

Step2: Find the reference angle

The reference angle $\theta'$ for an angle $\theta=\frac{3\pi}{4}$ in the second - quadrant is $\theta'=\pi - \frac{3\pi}{4}=\frac{\pi}{4}$.

Step3: Use the cosine value of the reference angle and the sign in the quadrant

We know that $\cos\frac{\pi}{4}=\frac{\sqrt{2}}{2}$. In the second - quadrant, cosine is negative. So, $\cos\frac{3\pi}{4}=-\cos\frac{\pi}{4}=-\frac{\sqrt{2}}{2}$.

Answer:

$-\frac{\sqrt{2}}{2}$