Question

the terminal side of an angle θ in standard position passes through the point (-5, -2). use the figure to find the following value.
r =
(type an exact answer in simplified form. rationalize all denominators.)

Explanation:

Step1: Recall the formula for \( r \)

For a point \((x, y)\) on the terminal side of an angle \(\theta\) in standard position, \( r=\sqrt{x^{2}+y^{2}} \). Here, \( x = - 5 \) and \( y=-2 \).

Step2: Substitute \( x \) and \( y \) into the formula

Substitute \( x=-5 \) and \( y = - 2 \) into \( r=\sqrt{x^{2}+y^{2}} \), we get \( r=\sqrt{(-5)^{2}+(-2)^{2}} \).

Step3: Calculate the values inside the square root

First, calculate \((-5)^{2}=25\) and \((-2)^{2} = 4\). Then \(25 + 4=29\). So \( r=\sqrt{29} \).

Answer:

\(\sqrt{29}\)