Trigonometric Equation: 2sin(2x) = 2cos(x)

[GuN]

Homework Statement

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

Homework Equations

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.

 

[jedishrfu]

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

 

[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.

 

[vela]

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

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

 

[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.

The system I showed you will not be your final answer.

 

[GuN]

Right, I double checked the notes and found I used the wrong radians.

I redid it and got (for the domain of [0, 2pi] ) pi/6, 5pi/6, pi/2 and 3pi/2.