Answer
c = 5
$\sin$$B$ = $\frac{4}{5}$
$\cos$$B$ = $\frac{3}{5}$
$\tan$$B$ = $\frac{4}{3}$
$\csc$$B$ = $\frac{5}{4}$
$\sec$$B$ = $\frac{5}{3}$
$\cot$$B$ = $\frac{3}{4}$
Work Step by Step
Pythagorean Theorem: c$^{2}$ = a$^{2}$ + b$^{2}$
c$^{2}$ = 3$^{2}$ + 4$^{2}$
c$^{2}$ = 9 + 16
c$^{2}$ = 25
c = $\sqrt 25$
c = 5
$\sin$$B$ = $\frac{opposite}{hypotenuse}$ = $\frac{b}{c}$ = $\frac{4}{5}$
$\cos$$B$ = $\frac{adjacent}{hypotenuse}$ = $\frac{a}{c}$ = $\frac{3}{5}$
$\tan$$B$ = $\frac{opposite}{adjacent}$ = $\frac{b}{a}$ = $\frac{4}{3}$
$\csc$$B$ = $\frac{hypotenuse}{opposite}$ = $\frac{c}{b}$ = $\frac{5}{4}$
$\sec$$B$ = $\frac{hypotenuse}{adjacent}$ = $\frac{c}{a}$ = $\frac{5}{3}$
$\cot$$B$ = $\frac{adjacent}{opposite}$ = $\frac{a}{b}$ = $\frac{3}{4}$
