# Thread: Trigonometric equation:

1. ## Trigonometric equation:

I am trying to find the solutions for this equation.
I have worked it twice and keep getting different answers. Can someone show me step by step how to work it?
sin(2x)-cos(x)=0

2. Originally Posted by cmr7
I am trying to find the solutions for this equation.
I have worked it twice and keep getting different answers. Can someone show me step by step how to work it?
sin(2x)-cos(x)=0
Recall that $\sin\left(2x\right)=2\sin\left(x\right)\cos\left(x \right)$

Thus, $\sin\left(2x\right)-\cos\left(x\right)=0\implies 2\sin\left(x\right)\cos\left(x\right)-\cos\left(x\right)=0\implies \cos\left(x\right)\left[2\sin\left(x\right)-1\right]=0$

Thus, either $\cos\left(x\right)=0$ or $2\sin\left(x\right)-1=0\implies \sin\left(x\right)=\tfrac{1}{2}$

Can you take it from here? Also, is there a restriction on x [i.e. $0\leq x\leq2\pi$]??

3. I think my brain is just fried and I am over thinking things tonight. No restrictions on x. Thank you for all for your help!