Answer
$\sin\alpha=\frac{y}{\sqrt{x^{2}+y^{2}}}$
$\cos\alpha=\frac{x}{\sqrt{x^{2}+y^{2}}}$
$\tan\alpha=\frac{y}{x}$
$\csc\alpha=\frac{\sqrt{x^{2}+y^{2}}}{y}$
$\sec\alpha=\frac{\sqrt{x^{2}+y^{2}}}{x}$
$\cot\alpha=\frac{x}{y}$
Work Step by Step
$\sin\alpha=\frac{opposite}{hypotenuse}=\frac{y}{\sqrt{x^{2}+y^{2}}}$
$\cos\alpha=\frac{adjacent}{hypotenuse}=\frac{x}{\sqrt{x^{2}+y^{2}}}$
$\tan\alpha=\frac{opposite}{adjacent}=\frac{y}{x}$
$\csc\alpha=\frac{hypotenuse}{opposite}=\frac{\sqrt{x^{2}+y^{2}}}{y}$
$\sec\alpha=\frac{hypotenuse}{adjacent}=\frac{\sqrt{x^{2}+y^{2}}}{x}$
$\cot\alpha=\frac{adjacent}{opposite}=\frac{x}{y}$
