Question

the terminal side of an angle θ in standard position passes through the point (-5, -3). use the figure to find the following value. cos θ

Explanation:

Step1: Find the value of $r$

The formula for $r$ (distance from the origin to the point $(x,y)$) is $r=\sqrt{x^{2}+y^{2}}$. Given $x = - 5$ and $y=-3$, then $r=\sqrt{(-5)^{2}+(-3)^{2}}=\sqrt{25 + 9}=\sqrt{34}$.

Step2: Use the cosine - definition

The definition of $\cos\theta$ in terms of $x$, $y$, and $r$ is $\cos\theta=\frac{x}{r}$. Substituting $x=-5$ and $r = \sqrt{34}$, we get $\cos\theta=\frac{-5}{\sqrt{34}}=-\frac{5\sqrt{34}}{34}$.

Answer:

$-\frac{5\sqrt{34}}{34}$