# Find x in Tan trig problem

1. Jun 13, 2010

### tonyviet

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

tan((π(x))/2) = √(3)/2

2. Relevant equations

3. The attempt at a solution
tan(x) = √(3)/2
x= π/6 + πn, since Tan has a period of π
This is where I'm stuck

2. Jun 13, 2010

### cronxeh

Re: Trigonometry

tan(pi*x/2) = sqrt(3)/2
pi*x/2 = arctan(sqrt(3)/2)

x = (2*arctan(sqrt(3)/2))/pi

What is required of you? Find x?

3. Jun 13, 2010

### tonyviet

Re: Trigonometry

Yea Find x

4. Jun 13, 2010

### cronxeh

Re: Trigonometry

Oh ok no problem

Last edited: Aug 21, 2010
5. Jun 13, 2010

### Mentallic

Re: Trigonometry

I also found an x in your name! Funny that.

Well since for $$tan(x)=\frac{\sqrt{3}}{2}$$

$$x=\frac{\pi}{6}+\pi n$$

Then if we instead have $$tan\left(\frac{\pi x}{2}\right)=\frac{\sqrt{3}}{2}$$

We end up with $$\frac{\pi x}{2}=\frac{\pi}{6}+\pi n$$

and now solve for x. Simple, no?

EDIT: $$tan(\pi/6)=1/\sqrt{3}$$, not $$\sqrt{3}/2$$. Since it's not a nice number, it's best to leave it as $$arctan(\sqrt{3}/2)$$

Last edited: Jun 13, 2010