Answer
$\sin \theta=\frac{3}{5}$
$\cos \theta=\frac{4}{5}$
$\tan \theta=\frac{3}{4}$
$\csc \theta=\frac{5}{3}$
$\sec \theta=\frac{5}{4}$
$\cot \theta=\frac{4}{3}$
Work Step by Step
We are given $x=20,y=15$
$x, y, r$ form a right-angled triangle so to find r we can apply the formula:
$x^2+y^2=r^2$
$\rightarrow z=\sqrt 20^2+15^2=25$
With $x=20, y=15, z=25$, thetrigonometric functions are
$\sin \theta=\frac{y}{r}=\frac{15}{25}=\frac{3}{5}$
$\cos \theta=\frac{x}{r}=\frac{20}{25}=\frac{4}{5}$
$\tan \theta=\frac{y}{x}=\frac{15}{20}=\frac{3}{4}$
$\csc \theta=\frac{1}{\sin \theta}=\frac{5}{3}$
$\sec \theta=\frac{1}{\cos \theta}=\frac{5}{4}$
$\cot \theta=\frac{x}{y}=\frac{4}{3}$
