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))=(\sin(-20^(\circ)))/(\cos(-20^(\circ)))=(-\sin(20^(\circ)))/(\cos(20^(\circ)))=-\tan 20^(\circ).`