Question

I’m trying to complete old assignments and i forgot how to do this one

Answer 1

Cosine of Double Angle

We can use any of these two formulas:

`\begin{gathered} cos(2\theta)=2cos^2(\theta)-1 \\ \\ cos(2\theta)=1-2sin^2(\theta) \end{gathered}`

We are given:

`sin(\theta)=(5)/(13)`

So we use the second formula:

`cos(2\theta)=1-2\left((5)/(13)\right)^2`

Operating:

`\begin{gathered} cos(2\theta)=1-2\left((25)/(169)\right) \\ \\ cos(2\theta)=1-(50)/(169)=(119)/(169) \end{gathered}`

Answer: 119/169