[7.4-5] cosine, sin, tangent
Right triangles and trigonometry
$$ \sin \theta = \frac{{\rm Opp}}{{\rm Hyp}}
= \frac yr$$
$$ \cos \theta = \frac{{\rm Adj}}{{\rm Hyp}} =\frac xr $$
$$ \tan \theta = \frac{{\rm Opp}}{{\rm Adj}} = \frac yx = \text{ Slope of line!}$$
Also useful:
Pythagoras' theorem: $$r^2=x^2+y^2.$$
On the unit circle, $r=1$, $x=\cos \theta$., and $y=\sin \theta$, so...
$$1=\sin^2\theta+\cos^2\theta.$$
Blank unit circle