Question

sin(\frac{5\pi}{4})

Explanation:

Step1: Use the angle addition formula

We know that \(\frac{5\pi}{4}=\pi+\frac{\pi}{4}\). According to the formula \(\sin(A + B)=\sin A\cos B+\cos A\sin B\), here \(A=\pi\), \(B = \frac{\pi}{4}\). So \(\sin(\frac{5\pi}{4})=\sin(\pi+\frac{\pi}{4})=\sin\pi\cos\frac{\pi}{4}+\cos\pi\sin\frac{\pi}{4}\)

Step2: Substitute the values of trigonometric functions

We know that \(\sin\pi = 0\), \(\cos\pi=- 1\), \(\sin\frac{\pi}{4}=\frac{\sqrt{2}}{2}\), \(\cos\frac{\pi}{4}=\frac{\sqrt{2}}{2}\).
Substituting these values into the above formula:

$$
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$$

Answer:

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