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Trig functions within Trig functions

  1. Jul 24, 2010 #1
    1. The problem statement, all variables and given/known data

    I'm given the problem: [tex]\int[/tex][tex]\frac{\sqrt{y^{2}-25}}{y}[/tex] dy

    2. Relevant equations

    I set y = 5sec(u), and solve for the subsitution.

    3. The attempt at a solution

    At the culmination of my solution, I achieve: 5tan(u) - 5u + C

    Here is my dilemma, u stands for arcsec([tex]\frac{y}{5}[/tex]) -- How do I deal with tan(arcsec(..)), or any "trig within trig" setup? I've gone all this time without actually ever figuring out how to solve for these.
  2. jcsd
  3. Jul 24, 2010 #2
    You can use a right-angled triangle to aid you in visualizing what is going on. For instance, arcsec(y/5) returns an angle in a right-angled triangle where the adjacent side is of length 5 and the hypotenuse is of length y. Then, you can easily calculate the tangent of that angle.
  4. Jul 24, 2010 #3
    I was previously using this as a method to solve them but I ran into a few instances of having different answers than the book. I'll look further into it, thank you for the response.
  5. Jul 26, 2010 #4


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    Homework Helper

    To comvert the tan into a sec.
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