How to solve this trig equation in radians 2sin^2(x) + sin(x) - 1=0

1. Sep 9, 2004

UrbanXrisis

I just got a review sheet in math that contain questions that I dont know how to do from last year. ONe asks to solve for all values of theta of [0,2pi] in radians: 2sin^2(theta)+sin(theta)-1=0

any ideas?

2. Sep 9, 2004

Leong

Use
$$sin\ 2\theta = 2\ sin\ \theta\ cos\ \theta$$
$$sin^2\ \theta + cos^2\ \theta = 1$$

3. Sep 9, 2004

UrbanXrisis

that confuses me more. I have no clue what the question is even asking, I think I forgot all my math. Could you give a longer explanation?

4. Sep 9, 2004

recon

Let $$sin\ \theta\ = x$$

Then your original equation now looks like $$2x^2 + x - 1 = 0$$.

Solve the quadratic equation. Once you do that, the rest should be easy.

5. Sep 9, 2004

Pyrrhus

The question is asking for which angles in a 0 to 2pi interval satisfy that equation.

-Cyclovenom

6. Sep 10, 2004

Leong

forget about what i have said. use recon's suggestion and understand cyclovenom's point.