Question

what is sin 5π/4?

Explanation:

Step1: Convert angle to reference angle

The angle \(\frac{5\pi}{4}\) is in the third quadrant. The reference angle \(\theta_{ref}=\frac{5\pi}{4}-\pi=\frac{\pi}{4}\).

Step2: Determine the sign of sine in the third quadrant

In the third quadrant, sine is negative.

Step3: Find the value of \(\sin\frac{\pi}{4}\)

We know that \(\sin\frac{\pi}{4}=\frac{\sqrt{2}}{2}\).

Step4: Combine the sign and the value

Since \(\sin\frac{5\pi}{4}\) is negative and has the same magnitude as \(\sin\frac{\pi}{4}\), \(\sin\frac{5\pi}{4}=-\frac{\sqrt{2}}{2}\)

Answer:

\(-\frac{\sqrt{2}}{2}\)