Answer
$\sin B=\frac{12}{13}$
$\cos B=\frac{5}{13}$
$\tan B=\frac{12}{5}$
$\csc B=\frac{13}{12}$
$\sec B=\frac{13}{5}$
$\cot B=\frac{5}{12}$
Work Step by Step
$c=\sqrt {a^{2}+b^{2}}=\sqrt {5^{2}+12^{2}}=13$
$\sin B=\frac{\text{side opposite}}{\text{hypotenuse}}=\frac{12}{13}$
$\cos B=\frac{\text{side adjacent}}{\text{hypotenuse}}=\frac{5}{13}$
$\tan B=\frac{\text{side opposite}}{\text{side adjacent}}=\frac{12}{5}$
The cosecant, secant, and cotangent ratios are reciprocals of the sine, cosine, and tangent values, respectively, so we have
$\csc B=\frac{13}{12}$
$\sec B=\frac{13}{5}$
$\cot B=\frac{5}{12}$
