Question

Find the cos(Θ) of an angle in standard position if the terminal side passes through the point (4, -8).

Note: Answer choices attached below

Answer 1

Look at the picture.

$r=\sqrt{x^2+y^2}-\text{from the Pythagorean theorem}\\\\\sin\theta=\dfrac{y}{r}\\\\\cos\theta=\dfrac{x}{r}\\\\\tan\theta=\dfrac{y}{x}\\\\\cot\theta=\dfrac{x}{y}$

We have the point

$(4,\ -8)\to x=4,\ y=-8$

Calculate r:

$r=\sqrt{4^2+(-8)^2}=\sqrt{16+64}=\sqrt{80}=\sqrt{16\cdot5}=\sqrt{16}\cdot\sqrt5=4\sqrt5$

Substitute:

$\cos\theta=\dfrac{4}{4\sqrt5}=\dfrac{1}{\sqrt5}\to\boxed{C)}$