Question

In two or more complete sentences, use your knowledge of the unit circle to describe why the following trigonometric equation is true.

tan(-20 degrees) = -tan(20 degrees)

Answer 1

You have to describe why $\tan (-20^{\circ})=-\tan 20^{\circ}.$

Consider the left side $\tan (-20^{\circ}).$ Angle $-20^{\circ}$ is placed at IVth quadrant and has (see attached diagram for signs of cosines - first sign in brackets and sines - second sign in brackets)

$\cos (-20^{\circ})=\cos (20^{\circ}),\\\sin (-20^{\circ})=-\sin (20^{\circ}).$

Then

$\tan (-20^{\circ})=\dfrac{\sin(-20^{\circ})}{\cos(-20^{\circ})}=\dfrac{-\sin(20^{\circ})}{\cos(20^{\circ})}=-\tan 20^{\circ}.$