Q. 23 - Precalculus Enhanced with Graphing Utilities

Question

the point (x, y) is on the terminal side of angle  in standard position. Find the exact value of the given trigonometric function

$(-5,11) , \cos \vartheta$

Step-by-Step Solution

Answer

$\cos \vartheta =\frac{-5}{\sqrt{146}}$

Step 1. Given information

$(-5,11) , \cos \vartheta$

Step 2. Solving for cos ϑ

We know that for any given point (x,y) 

$$\begin{gathered} \cos \vartheta = \frac{x}{r} \\ r=\sqrt{x^2+y^2} \end{gathered}$$

Using this :$$\begin{gathered} \cos \vartheta = \frac{x}{r} \\ \cos \vartheta = \frac{-5}{\sqrt{5^2+{11}^2}} \\ \cos \vartheta =\frac{-5}{\sqrt{146}} \end{gathered}$$