solve sin theta +1= cos 2theta on the interval theta is greater than or equal to 0 and less than 2pi

Answer 1

Hi Annette,

I am going to use A as the angle (instead of theta), but the workings are the same regardless of what symbol you use to represent the angle.

sin A + 1 = cos 2A

sin A + 1 = 1 - 2 * (sin A) ^ 2 (double angle formula)

sin A + 2 * (sin A) ^ 2 = 0

sin A (1 + 2 * sin A) = 0

sin A = 0 or 1 + 2 * sin A = 0

sin A = 0 or sin A = -1/2

with A ≥ 0 and < 2pi,

A = 0, or A = 7pi/6 or A = 11pi/6

Please let me know if you need further help.

Katherine