Question

Can someone explain how to do this? thank you!

Answer 1

The answer will be Negative

Write sin($\frac{5 \pi }{4}$) as sin($\pi$+$\frac{ \pi } {4}$)

Using the summation identity will be:
=sin($\pi$)+cos($\pi$)sin($\frac{ \pi }{4}$)

By following the trivial identity, you should get:
=0*$\frac{ \sqrt{2}}{2}+(-1) \frac{\sqrt 2} {2}$

Remove the parentheses on -1, then multiply
=0*$\frac{ \sqrt 2} {2}-1* \frac{ \sqrt 2} {2}$

You should get:
$- \frac{ \sqrt 2} {2}$