Question

Let `sinx=2/3`, how do you show that `f(2x)=-(4sqrt5)/9`?

Answer 1

see explanation below

Explanation:

`sin x = 2/3`, therefore by using Pythagoras theorem,
`cos x = sqrt 5/3`

if `f(x) = sin x`, then
`f(2 x) = sin 2 x`

`sin 2 x = 2 sin x cos x`

`sin 2 x = 2 * 2/3 *sqrt 5/3`

therefore,
`f (2 x) =sin 2 x = (4 sqrt 5)/9`