Question

Evaluatesin^-1 (sin3pi/4)Show your reasoning.

Answer 1

Answer:
`\sin ^(-1)(\sin (3\pi)/(4))=(\pi)/(4)`

Step-by-step explanation:

Given the expression:

`\sin ^(-1)(\sin (3\pi)/(4))`

The exact value of:

`\sin ((3\pi)/(4))=\frac{1}{\sqrt[]{2}}`

Then:

`\sin ^(-1)(\sin (3\pi)/(4))=\sin ^(-1)(\frac{1}{\sqrt[]{2}})`

Evaluating, we have:

`(\pi)/(4)`