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

Respuesta :

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

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

[tex]\cos(\alpha)=x,\quad\sin(\alpha)=y[/tex]

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