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:

$sin(\theta)=\frac{5}{13}$

So we use the second formula:

$cos(2\theta)=1-2\left(\frac{5}{13}\right)^2$

Operating:

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

Answer: 119/169