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
$c=\sqrt {a^{2}+b^{2}}=\sqrt {3^{2}+4^{2}}=5$
$\sin B=\frac{\text{side opposite}}{\text{hypotenuse}}=\frac{b}{c}=\frac{4}{5}$
$\cos B=\frac{\text{side adjacent}}{\text{hypotenuse}}=\frac{a}{c}=\frac{3}{5}$
$\tan B=\frac{\text{side opposite}}{\text{side adjacent}}=\frac{b}{a}=\frac{4}{3}$
The cosecant, secant, and cotangent ratios are reciprocals of the sine, cosine, and tangent values, respectively, so we have
$\csc B=\frac{5}{4}$
$\sec B=\frac{5}{3}$
$\cot B=\frac{3}{4}$
