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=√(x^2+y^2)-\text{from the Pythagorean theorem}\\\\\sin\theta=(y)/(r)\\\\\cos\theta=(x)/(r)\\\\\tan\theta=(y)/(x)\\\\\cot\theta=(x)/(y)`

We have the point

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

Calculate r:

`r=√(4^2+(-8)^2)=√(16+64)=√(80)=√(16\cdot5)=√(16)\cdot\sqrt5=4\sqrt5`

Substitute:

`\cos\theta=(4)/(4\sqrt5)=(1)/(\sqrt5)\to\boxed{C)}`