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Math Help - Find Critical numbers

  1. #1
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    Find Critical numbers

    Find any critical numbers of: f(theta) = 2sec(theta) + tan(theta), 0<theta<2pi.
    I found the defivative, but I got stuck.

    I got to 2tan(theta)=-sin(theta).
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  2. #2
    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by unluckykc View Post
    Find any critical numbers of: f(theta) = 2sec(theta) + tan(theta), 0<theta<2pi.
    I found the defivative, but I got stuck.

    I got to 2tan(theta)=-sin(theta).
    and how did you get to that answer? what is the derivative of \sec \theta and \tan \theta?
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  3. #3
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    Oh, sorry. I got to include the steps.
    f'(theta) = 2sec(theta)tan(theta) + sec^2(theta)
    I set it equal to zero, factored out a sec(theta). I was left with 2 equations: sec(theta)=0 and 2tan(theta) + sec(theta) = 0 =>2tan(theta) = -sec(theta) {I didn't mean sin before...I meant sec}
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    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by unluckykc View Post
    Oh, sorry. I got to include the steps.
    f'(theta) = 2sec(theta)tan(theta) + sec^2(theta)
    I set it equal to zero, factored out a sec(theta). I was left with 2 equations: sec(theta)=0 and 2tan(theta) + sec(theta) = 0 =>2tan(theta) = -sec(theta) {I didn't mean sin before...I meant sec}
    ok. and you are aware that \sec \theta is never zero, correct?

    anyway, here's how i would proceed.

    2 \tan \theta + \sec \theta = 0

    \Rightarrow \frac {2 \sin \theta }{\cos \theta} + \frac 1{\cos \theta } = 0

    now combine the fractions and set the numerator equal to zero and solve for theta
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