Question

use reference angles to find the exact value of the following expression. sin(5π/4) select the correct choice below and, if necessary, fill in the answer box to complete your choice. a. sin(5π/4) = (simplify your answer. type an exact answer, using radicals as needed. use integers or fractions for any numbers in the b. the answer is undefined.

Explanation:

Step1: Determine the quadrant

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

Step2: Find the reference angle

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

Step3: Determine the sign of sine in the third - quadrant

In the third - quadrant, the sine function is negative.

Step4: Evaluate the sine of the reference angle

We know that $\sin\frac{\pi}{4}=\frac{\sqrt{2}}{2}$. Since $\sin\theta$ is negative in the third - quadrant for $\theta = \frac{5\pi}{4}$, then $\sin\frac{5\pi}{4}=-\frac{\sqrt{2}}{2}$.

Answer:

A. $\sin\frac{5\pi}{4}=-\frac{\sqrt{2}}{2}$