Question

How do you find the exact value of $\sin \left(\frac{\mathrm{\pi }}{3}\right)$ ?

Answer 1

Compute the required value.

Convert the angle from radians to degrees.

$$\begin{gathered} \mathrm{Sin}\left(\frac{\mathrm{\pi }}{3}\right)=\mathrm{Sin}\left(\frac{\mathrm{\pi }\times 180°}{3\times \mathrm{\pi }}\right) \\ \Rightarrow \mathrm{Sin}\left(\frac{\mathrm{\pi }}{3}\right)=\mathrm{Sin}\left(60°\right) \end{gathered}$$

From the standard trigonometric table,

$\mathrm{Sin}(60°)=\frac{\sqrt{3}}{2}$

Hence, the value of $\sin \left(\frac{\mathrm{\pi }}{3}\right)$ is$\frac{\sqrt{3}}{2}$.