Question

Can someone explain how to do this? thank you!

Answer 1

The answer will be Negative

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

Using the summation identity will be:
=sin(
`\pi`)+cos(
`\pi`)sin(
`( \pi )/(4)`)

By following the trivial identity, you should get:
=0*
`( √(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}`