Question

Find the value of the trigonometric function $\sin 765°$.

Answer 1

Calculate the value of the trigonometric function.

The given trigonometric function is $\sin 765°$.

Expand the angle $765°$ as $720°+45°$ to simplify the calculation.

$\begin{array}{rcl}\sin 765°& =& \sin \left(720°+45°\right)\\ & =& \sin \left(2\times 360°+45°\right)\\ & & \\ & =& \sin 45°[\because \sin (n\times 360°+\varnothing )=\sin \varnothing ]\\ & =& \frac{1}{\sqrt{2}}\end{array}$

Hence, the required final answer is $\frac{1}{\sqrt{2}}$.