How does the unit circle allow the trigonometric functions to be defined for all real numbers instead of just for acute angles?

Question

asked Aug 1, 2021 199k views

1 Answer

Igor Damiani · Answer 1 · 2021-08-06T02:33:50+0000

Every point in the unit circle is identified either by its coordinates
(x,y) or by the angle it forms with the x-axis,
$\alpha$ .

The trigonometric functions associate with every angle
$\alpha$ and the correspondant
(x,y) coordinates the two values

$\cos(\alpha)=x,\quad\sin(\alpha)=y$

This procedure can be done for every angle
$\alpha$ , so you don't have to work with acute angles only.