# Arcsec problem [trigonometry]

1. Feb 15, 2009

### Firestrider

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

arcsec([2 * sqrt(3)] / 3)

2. Relevant equations
N/A

3. The attempt at a solution
I know that this is equivalent to saying sec (theta) = [2 * sqrt(3)] / 3
I don't know how to solve for theta in terms of PI.

I know sec = hyp/adj and the opp side I found was sqrt(3).
When I try to do this in the calculator I get a DOMAIN error, and even if I did get an angle it would not be a whole number, how to I convert this in terms of PI?

2. Feb 15, 2009

### rock.freak667

If $sec\theta= \frac{2\sqrt{3}}{3}$
That means that cos$\theta$ = ?

Also note that $\frac{\sqrt{3}}{3}=\frac{1}{\sqrt{3}}$

3. Feb 15, 2009

### Firestrider

Yeah, I know cos (theta) = sqrt(3)/3 but I don't know how to find the angle. All the unit circles I see don't give that reference.

4. Feb 16, 2009

### HallsofIvy

Staff Emeritus
No, you do NOT "know cos (theta) = sqrt(3)/3"! What happened to the 2 in "[2 * sqrt(3)] / 3"?

If $sec(\theta)= \frac{2\sqrt{3}}{3}$ then $cos(\theta)= \frac{3}{2\sqrt{3}}$
NOW use what rock.freak667 said.

Last edited: Feb 16, 2009