# Homework Help: Trigonometric equation

1. Sep 16, 2013

### GuN

1. The problem statement, all variables and given/known data

2 sin(2x) = 2 cos(x)

2. Relevant equations

3. The attempt at a solution

4sinxcosx-2cosx=0

2(2sinxcosx-cosx)=0

2cosx(sinx-1)=0

2cosx=0 sinx=1

And then I did the math and got pi/2 and 3pi/2 , but that's apparently wrong.
1. The problem statement, all variables and given/known data

2. Relevant equations

3. The attempt at a solution

2. Sep 16, 2013

### Staff: Mentor

I get cosx * (2*sinx - 1) = 0 for your second to last step. Does that help?

3. Sep 16, 2013

### GuN

I still get pi/2 and 3 pi/2.

>_<

I'll try consulting my notes on how to properly calculate cosx=0 and sinx=1/2.

4. Sep 16, 2013

### vela

Staff Emeritus
How? You know that $\sin (\pi/2) = 1$ and $\sin (3\pi/2) = -1$. So obviously neither of those satisfy $\sin x = 1/2$.

5. Sep 16, 2013

### lendav_rott

arcsin (1/2) = x1
arccos (0) = x2

You have done everything correctly, now you need to figure out what the values for x are. This is not a linear equation, there are 2 series of solutions.