Finding the Angle Using Arcsec in Trigonometry

[Firestrider]

Homework Statement

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

Homework Equations

N/A

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?

 

[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}}

 

[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.

 

[HallsofIvy]

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.