# Analytic Trigonometry

1. Jan 8, 2012

### darshanpatel

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

Find all the solutions of each equation in the interval (0, 2∏)

cos(2x)=1/2

2. Relevant equations

-None-

3. The attempt at a solution

cos(2x)=1/2
2x=(cos^(-1))*1/2
2x= ((∏)/3), ((5∏)/3)
2x= ((∏)/3), ((5∏)/3), ((14∏)/6)
x= ∏/6, ((5∏)/6),

That's all I have.

I know there is one more solution, but I don't know how to find it.

2. Jan 8, 2012

### Curious3141

Sure there's just the one more?

You're asked to find x in (0,2∏). What's the corresponding range of 2x?

You know that cosine has period 2∏. Can you use this to figure out what other values 2x can take, and the corresponding x values?

3. Jan 8, 2012

### darshanpatel

What do you mean by corresponding range of 2x? I don't understand...

4. Jan 8, 2012

### Curious3141

If min(x) = 0, max(x) = 2pi, what are the corresponding min and max values 2x can take? Start with that. That way you'll know what values of 2x to consider when you take the inverse cosine of 0.5