7.7 homework #8 find the exact value of cos 5π/4. 15 fill in the blank 1 point what quadrant is the angle…

Explanation:

Step1: Determine the quadrant

The angle $\theta=\frac{5\pi}{4}$. Since $\pi<\frac{5\pi}{4}<\frac{3\pi}{2}$, the angle is in the third - quadrant.

Step2: Find the reference angle

The reference angle $\theta_{r}$ for an angle $\theta$ in the third - quadrant is $\theta_{r}=\theta-\pi$. So, $\theta_{r}=\frac{5\pi}{4}-\pi=\frac{\pi}{4}$.

Step3: Evaluate the cosine

In the third - quadrant, cosine is negative. And $\cos\frac{\pi}{4}=\frac{\sqrt{2}}{2}$, so $\cos\frac{5\pi}{4}=-\frac{\sqrt{2}}{2}$.

Answer:

The angle is in the third - quadrant. The reference angle is $\frac{\pi}{4}$. The value of $\cos\frac{5\pi}{4}=-\frac{\sqrt{2}}{2}$