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Theta in converting sec to cos

  1. Nov 5, 2011 #1
    1. The problem statement, all variables and given/known data
    I saw in my calculus book that something along the lines of arcsec [itex]\frac{4}{\sqrt{pi}}[/itex] = x was converted to arccos [itex]\frac{\sqrt{pi}}{4}[/itex] = x. I understand that sec and cos are reciprocals, but I don't see why has to be flipped as well.

    2. Relevant equations
    cos (θ), sec (θ)


    3. The attempt at a solution
    I began to think of the graphs and such, but I just can't think of why this works. I don't normally mess with the inverse trig functions and was hoping someone could point out what I'm missing.

    Thank you.
     
  2. jcsd
  3. Nov 5, 2011 #2

    Mark44

    Staff: Mentor

    Let x = [itex]sec^{-1}\frac{4}{\sqrt{\pi}}[/itex]
    Then sec(x) = [itex]\frac{4}{\sqrt{\pi}}[/itex]
    So cos(x) = [itex]\frac{\sqrt{\pi}}{4}[/itex]
    Which means that x = cos-1[itex]\frac{\sqrt{\pi}}{4}[/itex]

    It should be understood that there are domain restrictions on x.
     
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