Question

Determine the solutions to the equation 2sinx − cos2x = sin2x for 0 ≤ x ≤ 2π .

How do I start this question?

Answer 1

do you mean sin(2x) or sin^2 x ???

Answer 2

Sorry, I meant 2sinx - cos^2x = sin^2x for 0 ≤ x ≤ 2π

2sinx - cos^2x = sin^2x


Do I change the left side to

2sinxcosx - cos^2x = sin^2x

Answer 3

2 sin x = sin^2 x + cos^2 x = 1

Answer 4

sin^2 x + cos^2 x = 1 VERY IMPORTANT trig identity

Answer 5

sin x = 1/2
x = 30 degrees or 150 degrees

Answer 6

Thank you~

May I know how you got 150 degrees? I am so confused when finding the reference angles, whether to subtract or add the degrees.

Answer 7

well I just looked for 30 degrees above and below the x and - x axis and picked the one where sin was positive. That is in quadrants 1 and 2. 180-30 = 150

Answer 8

Thank you!