Use identities to find values of sin 2θ and cos 2θ for cos θ = -12/13, sin θ > 0

Question

Could anyone help me solve this problem? I have been stuck on it for a while. 

Answer 1

To solve this problem, you need to know the following

sin2θ = 2sinθcosθ       (1)

cos2θ = cos²θ - sin²θ (2)

sin²θ + cos²θ = 1       (3)

 

From equation (3) sinθ = ±SQRT(1-cos²θ) = ±5/13.  You choose 5/13 since the problem states that sinθ > 0.

Plug the value of sinθ that we just found and the given value for cosθ into equations (1) and (2) to get sin2θ and cos2θ.

 

To do well, you really need to know the above trigonometric identities and a few more.  Just write them LARGE in INK on a piece of paper and tape it to the wall near your bed or desk.  Have fun!