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Homework Help: Solve a Trig Equation Containing secant

  1. Nov 13, 2013 #1
    1. The problem statement, all variables and given/known data

    sec(5x)-5=0
    2. Relevant equations



    3. The attempt at a solution


    I turned it into 1/cos(5x)=5 x=θ/5
    then i switched it to cos(5x)=/1/5

    Then cos-1(1/5)=θ which = 1.36 (one solution) then divided by 5 which is .2738 which works as one solution
    since the positive cos is in the 1st and 4th quadrant i need to subtract 2pi to 1.36= 4.91 then divide by 5 which gives me .9827 which also works

    But i am stuck after that
     
    Last edited: Nov 13, 2013
  2. jcsd
  3. Nov 13, 2013 #2

    Mark44

    Staff: Mentor

    And lost your equation.

    You're making this harder than it needs to be. If 1/cos(5x) = 5, then cos(5x) = 1/5.

    You could also say that cos(5x + k*2##\pi##) = 1/5, and since cosine is positive in Q IV, you could also say that cos(-5x + k*2##\pi##) = 1/5, where k is an integer.

    Now you can take cos-1 of both sides.
     
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