Question

Cos
`\alpha`=
`(5)/(13)` where
`270\leq \alpha \leq 360`.

Find cos 2
`\alpha`

Answer 1

-119/169

Explanation:

You want cos(2α) where cos(α) = 5/13 and 270° < α < 360°.

Cosine identity

The desired function is ...

cos(2α) = 2cos²(α) -1

Application

In the given quadrant, sin(α) < 0. Since the sine is squared in the double-angle identity, whether it is positive or negative is irrelevant.

`\cos(2\alpha)=2\cos^2(\alpha)-1=2\left((5)/(13)\right)^2-1=(2(25)-169)/(169)\\\\\boxed{\cos(2\alpha)=-(119)/(169)}`