Answer
$\sin\alpha=\frac{x}{\sqrt{x^{2}+1}}$
$\cos\alpha=\frac{1}{\sqrt{x^{2}+1}}$
$\tan\alpha=x$
$\csc\alpha=\frac{\sqrt{x^{2}+1}}{x}$
$\sec\alpha=\sqrt{x^{2}+1}$
$\cot\alpha=\frac{1}{x}$
Work Step by Step
Let $l$ be the length of the side with an unknown length.
$l=\sqrt{(\sqrt{x^{2}+1})^{2}-x^{2}}$
$l=\sqrt{x^{2}+1-x^{2}}$
$l=\sqrt{1}$
$l=1$
$\sin\alpha=\frac{opposite}{hypotenuse}=\frac{x}{\sqrt{x^{2}+1}}$
$\cos\alpha=\frac{adjacent}{hypotenuse}=\frac{1}{\sqrt{x^{2}+1}}$
$\tan\alpha=\frac{opposite}{adjacent}=\frac{x}{1}=x$
$\csc\alpha=\frac{hypotenuse}{opposite}=\frac{\sqrt{x^{2}+1}}{x}$
$\sec\alpha=\frac{hypotenuse}{adjacent}=\frac{\sqrt{x^{2}+1}}{1}=\sqrt{x^{2}+1}$
$\cot\alpha=\frac{adjacent}{opposite}=\frac{1}{x}$
