[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