Question

If `x + 2 = 3sintheta`, how do you determine the value of `cos(2theta)`?

Answer 1

`cos(2theta) = 1 - 2/9(x + 2)^2`

Explanation:

We know that `cos(2theta) = cos(theta + theta) = cos^2theta - sin^2theta = 1 - 2sin^2theta`

From our initial equation, we see that `(x + 2)/3 = sintheta`.

Therefore,

`cos(2theta) = 1 - 2((x+ 2)/3)^2`

`cos(2theta) = 1 - 2/9(x + 2)^2`

Hopefully this helps!