Question

How do you find the value of `sin2theta` given `costheta=1/3` and `0<theta<90`?

Answer 1

`= (4sqrt(2) ) / 9`

Explanation:

`sin^2 theta + cos^2 theta = 1`

`=> sin theta = sqrt(1 - cos^2 theta )`

`=> sin theta = (2sqrt(2) ) / 3`

`sin 2 theta = 2 sin theta cos theta`

`= 2 * 1/3 * ( 2sqrt(2) ) / 3`

`= (4sqrt(2) ) / 9`