Answer
$b=\sqrt {2}$
$\sin B=\frac{\sqrt {2}}{2}$
$\cos B=\frac{\sqrt 2}{2}$
$\tan B=1$
$\csc B=\sqrt {2}$
$\sec B=\sqrt 2$
$\cot B=1$
Work Step by Step
$b=\sqrt {c^{2}-a^{2}}=\sqrt {2^{2}-(\sqrt {2})^{2}}=\sqrt {2}$
$\sin B=\frac{\text{side opposite}}{\text{hypotenuse}}=\frac{b}{c}=\frac{\sqrt {2}}{2}$
$\cos B=\frac{\text{side adjacent}}{\text{hypotenuse}}=\frac{a}{c}=\frac{\sqrt 2}{2}$
$\tan B=\frac{\text{side opposite}}{\text{side adjacent}}=\frac{b}{a}=\frac{\sqrt {2}}{\sqrt {2}}=1$
The cosecant, secant, and cotangent ratios are reciprocals of the sine, cosine, and tangent values, respectively, so we have
$\csc B=\frac{2}{\sqrt {2}}=\sqrt {2}$
$\sec B=\frac{2}{\sqrt 2}=\sqrt 2$
$\cot B=1$
