# Homework Help: Help Understanding Trig Equation

1. Apr 22, 2012

### theintarnets

1. The problem statement, all variables and given/known data
Find all possible solutions:
2cos22θ = 1 - cos2θ

3. The attempt at a solution
I know all my arithmetic is correct, but when it comes to giving the answer, I'm not sure how to write it.
2cos22θ + cos2θ - 1 = 0
(2cos2θ - 1)(cos2θ + 1) = 0
2cos2θ = 1
cos2θ = 1/2
2θ = ∏/3

cos2θ = -1
2θ = ∏

So θ is equal to ∏/6 and ∏/2
But the solutions are supposed to be:
∏/6 + ∏n
5∏/6 + ∏n
∏/2 + ∏n
And I don't understand why. Can someone explain it to me please?

2. Apr 22, 2012

### SammyS

Staff Emeritus
It's because the cosine function is periodic and is an even function.

3. Apr 22, 2012

### theintarnets

Even as in cos(-x) = cos x? What do you mean by periodic? Thanks!

4. Apr 22, 2012

### SammyS

Staff Emeritus
cos(x) = cos(x + 2π) = cos(x + 4π) = cos(x + 2πk) , where k is an integer.

5. Apr 23, 2012

### theintarnets

Ohhhhhh, I see, thank you! What is sin(x) then, because I know sin is odd, but I'm not sure how that looks.

6. Apr 24, 2012

### Bohrok

An odd function means that f(-x) = -f(x). Graphically, f(-x) is just f(x) flipped across the x-axis or y-axis. Also, f(x) has rotational symmetry in that it's unchanged if you rotate it 180°.