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Arcsec problem [trigonometry]

  1. Feb 15, 2009 #1
    1. The problem statement, all variables and given/known data

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

    2. Relevant equations

    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. jcsd
  3. Feb 15, 2009 #2


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    Homework Helper

    If [itex]sec\theta= \frac{2\sqrt{3}}{3}[/itex]
    That means that cos[itex]\theta[/itex] = ?

    Also note that [itex]\frac{\sqrt{3}}{3}=\frac{1}{\sqrt{3}}[/itex]
  4. Feb 15, 2009 #3
    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.
  5. Feb 16, 2009 #4


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    Science Advisor

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

    If [itex]sec(\theta)= \frac{2\sqrt{3}}{3}[/itex] then [itex]cos(\theta)= \frac{3}{2\sqrt{3}}[/itex]
    NOW use what rock.freak667 said.
    Last edited by a moderator: Feb 16, 2009
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