Calculus 8th Edition

$sin \alpha=\frac{2\sqrt 5}{5}$ $cos \alpha=\frac{\sqrt 5}{5}$ $csc \alpha=\frac{\sqrt 5}{2}$ $sec \alpha=\sqrt 5$ $cot \alpha=\frac{1}{2}$
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: $sin \alpha=\frac{2\sqrt 5}{5}$ $cos \alpha=\frac{\sqrt 5}{5}$ $csc \alpha=\frac{\sqrt 5}{2}$ $sec \alpha=\sqrt 5$ $cot \alpha=\frac{1}{2}$