Given a trigonometric function to evaluate
[tex]\sin (\frac{23\pi}{4})[/tex]
We know the trigonometric identity:
[tex]\sin (2n\pi-\theta)=-\sin \theta[/tex]
The given function can be rewritten as:
[tex]\begin{gathered} \sin (\frac{23\pi}{4})=\sin (6\pi-\frac{\pi}{4}) \\ =\sin (2\times3\times\pi-\frac{\pi}{4}) \\ =-\sin (\frac{\pi}{4}) \\ =-\frac{1}{\sqrt[]{2}} \end{gathered}[/tex]
Thus, the answer is:
[tex]-\frac{1}{\sqrt[]{2}}[/tex]
