Answer
$\sin\alpha=\frac{x}{\sqrt{x^{2}+4}}$
$\cos\alpha=\frac{2}{\sqrt{x^{2}+4}}$
$\tan\alpha=\frac{x}{2}$
$\csc\alpha=\frac{\sqrt{x^{2}+4}}{x}$
$\sec\alpha=\frac{\sqrt{x^{2}+4}}{2}$
$\cot\alpha=\frac{2}{x}$
Work Step by Step
Let $l$ be the length of the side with an unknown length.
$l=\sqrt{x^{2}+2^{2}}$
$l=\sqrt{x^{2}+4}$
$\sin\alpha=\frac{opposite}{hypotenuse}=\frac{x}{\sqrt{x^{2}+4}}$
$\cos\alpha=\frac{adjacent}{hypotenuse}=\frac{2}{\sqrt{x^{2}+4}}$
$\tan\alpha=\frac{opposite}{adjacent}=\frac{x}{2}$
$\csc\alpha=\frac{hypotenuse}{opposite}=\frac{\sqrt{x^{2}+4}}{x}$
$\sec\alpha=\frac{hypotenuse}{adjacent}=\frac{\sqrt{x^{2}+4}}{2}$
$\cot\alpha=\frac{adjacent}{opposite}=\frac{2}{x}$
