Chapter 5 - Trigonometric Functions - Section 5.3 Properties of the Trigonometric Functions - 5.3 Assess Your Understanding - Page 418: 37

$\tan{\theta}=2$ $\csc{\theta} =\dfrac{\sqrt{5}}{2}$ $\sec{\theta} =\sqrt{5}$ $\cot{\theta} = \dfrac{1}{2}$

$\tan{\theta}= \dfrac{\sin{\theta}}{\cos{\theta}}$ $\therefore \tan{\theta}= \dfrac{\dfrac{2\sqrt{5}}{5}}{\dfrac{\sqrt{5}}{5}}=2$ $\csc{\theta} = \dfrac{1}{\sin{\theta}}$ $\therefore \csc{\theta} = \dfrac{1}{\dfrac{2\sqrt{5}}{5}}=\dfrac{\sqrt{5}}{2}$ $\sec{\theta} = \dfrac{1}{\cos{\theta}}$ $\therefore \sec{\theta} = \dfrac{1}{\dfrac{\sqrt{5}}{5}}= \sqrt{5}$ $\cot{\theta} = \dfrac{1}{\tan{\theta}}$ $\cot{\theta} = \dfrac{1}{2}$