Question

Find the exact value. Do not use a calculator.

$\sin \frac{11\mathrm{\pi }}{2}$

Short answer

$\sin \frac{11\mathrm{\pi }}{2}=-1$

Step-by-step solution

Step 1. Given information

$\sin \frac{11\mathrm{\pi }}{2}$

Step 2. Unit circle

$$\begin{gathered} \mathrm{Rotate}\mathrm{anticlockwise}\mathrm{to}\mathrm{form}\frac{11\mathrm{\pi }}{2}\mathrm{angle}\mathrm{with}\mathrm{the}\mathrm{positive}\mathrm{x}-\mathrm{axis}. \\ \mathrm{The}\sin \frac{11\mathrm{\pi }}{2}\mathrm{equals}\mathrm{the}\mathrm{y}-\mathrm{coordinate}(-1)\mathrm{of}\mathrm{the}\mathrm{point}\mathrm{of}\mathrm{intersection}(0,-1)\mathrm{of}\mathrm{unit}\mathrm{circle}. \end{gathered}$$

Step 3. Final answer

$\sin \frac{11\mathrm{\pi }}{2}=\mathrm{y}=-1$