Question

Rewrite the expression in terms of the given angle's reference angle; then evaluate the result. Write the exact answer. Do not round.2311**(**)sin

Answer 1

Given a trigonometric function to evaluate

`\sin ((23\pi)/(4))`

We know the trigonometric identity:

`\sin (2n\pi-\theta)=-\sin \theta`

The given function can be rewritten as:

`\begin{gathered} \sin ((23\pi)/(4))=\sin (6\pi-(\pi)/(4)) \\ =\sin (2*3*\pi-(\pi)/(4)) \\ =-\sin ((\pi)/(4)) \\ =-\frac{1}{\sqrt[]{2}} \end{gathered}`

Thus, the answer is:

`-\frac{1}{\sqrt[]{2}}`