# Squared trigonometrics

1. May 10, 2007

### disregardthat

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

Hi, I wonder how to solve, and how to get the correct answer\answers to these types of problems:

$$2 \sin^2{x} - 4 \cos^2{x} = 0$$ $$x \in [0°,360°]$$

There are many answers to this. I would really like to know how the correct way to get all of them.

2. Relevant equations

I do not know any relevant equations for this.

3. The attempt at a solution

I have tryed to divide them with $$\cos^2(x)$$ to get $$\tan^2(x)$$ But it has not worked.

2. May 10, 2007

### cristo

Staff Emeritus
Well, firstly can you reduce the expression to contain only one of sinx or cosx by using the relationship sin2x+cos2x=1?

3. May 10, 2007

### disregardthat

No, I do not know how to do it! :\

4. May 10, 2007

### HallsofIvy

Staff Emeritus
Then you need to learn algebra! Since sin2x+ cos2x= 1, cos2x= 1- sin2x. Now replace cos2x in your equation by 1- sin2 x.

5. May 10, 2007

### disregardthat

Oh, I misunderstood. Of course...

I found this equation:

$$\cos^2(x) = \frac{1}{3}$$ But how do get all the answers? There are four.

If i square root bot sides, I will get two answers, (which are correct) but not all of them... How is the right way?

6. May 10, 2007

### disregardthat

I just found out, I took the square root, and the answer must also be negative...