Question

What is $\sin (-\theta )$ in terms of $\sin \theta$?

Answer 1

Trigonometric ratio:

We have, $\sin (-\theta )$, the angle $-\theta$ lies in the fourth quadrant.

And in the fourth quadrant $\sin \theta$ is negative.

$\therefore \sin (-\theta )=-\sin \theta$

Hence, $\mathbf{sin}\mathbf{}\mathbf{(}\mathbf{-}\mathbf{\theta }\mathbf{)}\mathbf{=}\mathbf{-}\mathbf{sin}\mathbf{}\mathbf{\theta }$