Question

Finding values of trigonometric functions given information about an angle:

Answer 1

Given:

`(x,y)=(2,-\sqrt[]{5})`
`\begin{gathered} r=\sqrt[]{x^2+y^2} \\ r=\sqrt[]{(2)^2+(-\sqrt[]{5})^2} \\ r=\sqrt[]{4+5} \\ r=\sqrt[]{9} \\ r=3 \end{gathered}`
`\begin{gathered} \cos \theta=(x)/(r) \\ =(2)/(3) \end{gathered}`
`\begin{gathered} \csc \theta=(r)/(y) \\ =\frac{3}{-\sqrt[]{5}} \\ =-\frac{3}{\sqrt[]{5}} \end{gathered}`
`\begin{gathered} \tan \theta=\frac{-\frac{\sqrt[]{5}}{3}}{(2)/(3)} \\ =-\frac{\sqrt[]{5}}{2} \end{gathered}`