Question

cos(2a) = what? I understand you use the formulas but I don't know how to get the hyp and what to do from there.

Answer 1

First, we find the hypotenuse using pythagoras theorem.

Observe the figure adjacent side is 7 and opposite side is 24. So:

`\begin{gathered} hypotenuse=\sqrt[]{(opposite)^2+(adjacent)^2} \\ \text{hypotenuse}=\sqrt[]{24^2+7^2} \\ hypotenuse=\sqrt[]{576+49} \\ \text{hypotenuse}=\sqrt[]{625} \\ \text{hypotenuse}=25 \end{gathered}`

From basic trigonometric ratio's:

`\cos \alpha=(adjacent)/(hypotenuse)=(7)/(25)`

Next, find the value of cos(2α). Apply the double angle formula:

`\cos (2\alpha)=2\cos ^2(\alpha)-1`

Therefore:

`\cos (2\alpha)=2((7)/(25))^2-1=2((49)/(625))-1=(98)/(625)-1=-(527)/(625)`

Answer:

`\cos (2\alpha)=-(527)/(625)`