Answer
$sin \alpha=\frac{2\sqrt 5}{5}$
$cos \alpha=\frac{\sqrt 5}{5}$
$csc \alpha=\frac{\sqrt 5}{2}$
$sec \alpha=\sqrt 5$
$cot \alpha=\frac{1}{2}$
Work Step by Step
Since $tan \alpha=2$, we can label the opposite side as having length 2 and the adjacent side as having length 1.
Then Pythagorean Theorem gives
hypotenuse side $=\sqrt {2^{2}+1^{2}}=\sqrt 5$
The other five trigonometric functions are given as follows:
$sin \alpha=\frac{2\sqrt 5}{5}$
$cos \alpha=\frac{\sqrt 5}{5}$
$csc \alpha=\frac{\sqrt 5}{2}$
$sec \alpha=\sqrt 5$
$cot \alpha=\frac{1}{2}$
