Question

find the exact value.
cos\frac{3\pi}{4}
type + or -
?\frac{\sqrt{}}{}

Explanation:

Step1: Determine the quadrant

$\frac{3\pi}{4}$ is in the second quadrant where cosine is negative.

Step2: Use reference angle

The reference angle for $\frac{3\pi}{4}$ is $\pi-\frac{3\pi}{4}=\frac{\pi}{4}$.
We know that $\cos\frac{\pi}{4}=\frac{\sqrt{2}}{2}$.
Since $\cos\frac{3\pi}{4}$ is negative (from step 1), so $\cos\frac{3\pi}{4}=-\frac{\sqrt{2}}{2}$.

Answer:

• $\frac{\sqrt{2}}{2}$