Question

Given `sin theta = (-12/13)`, and `cos theta > 0`, how do you find the exact values of sin(2theta) and cos(2theta)?

Answer 1

`sin2theta=-120/169` and `cos2theta=-119/169`

Explanation:

As `sintheta=-12/13` i.e. negative and `costheta` is positive, `theta` lies in `Q4` i.e. `(3pi)/2< theta < 2pi`

`costheta=sqrt(1-(-12/13)^2)-sqrt(1-144/169)=sqrt(25/169)=5/13`

Hence, `sin2theta=2sinthetacostheta=2xx(-12/13)xx5/13=-120/169`

and `cos2theta=cos^theta-sin^2theta=25/169-144/169=-119/169`