Find the exact value of cos theta in simplest radical form given an angle in standa...

1. Identify the coordinates: The problem states that the terminal side of angle $\theta$ passes through the point $(-35, 12)$. This means $x = -35$ and $y = 12$.

2. Calculate the distance r: The distance $r$ from the origin to the point $(x, y)$ is calculated using the Pythagorean theorem: $r = \sqrt{x^2 + y^2}$.
Substitute the given values: $r = \sqrt{(-35)^2 + (12)^2}$
$r = \sqrt{1225 + 144}$
$r = \sqrt{1369}$
$r = 37$

3. Determine the cosine value: The cosine of an angle in standard position is defined as $\cos \theta = \frac{x}{r}$.
Substitute the values of $x$ and $r$: $\cos \theta = \frac{-35}{37}$

1. Simplify the result: The fraction $\frac{-35}{37}$ is already in its simplest form, and it does not contain any radicals.