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Thread: Trigonometric Substitutions

  1. #1 Trigonometric Substitutions 
    Forum Freshman Wilhelm's Avatar
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    I keep having trouble with my trigonometric substitutions.

    take for example:

    integral from 0 to 1: dx / sqrt(1-x^2) (this also an improper integral)

    Here's what I'm doing:

    x=sin(t) dx=cos(t)

    1-x^2 = cos(t)^2 <--trig identity of 1-sin^2 = cos^2

    so now I have:

    cos(t)/sqrt(cos(t)^2) which gives me:

    cos(t)/ abs(cos(t)) = 1

    however, i'm making a mistake. where?


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  3. #2  
    Forum Freshman Wilhelm's Avatar
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    i think it might have something to do with inverse trigonometric functions...


    ...can you guys understand the way I typed the eq?


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  4. #3 Re: Trigonometric Substitutions 
    Forum Professor wallaby's Avatar
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    Quote Originally Posted by Wilhelm
    x=sin(t) dx=cos(t)
    if x=sin(t) then dx/dt = cos(t), thus dx = cos(t)dt
    which changes your result to be cos(t)dt/cos(t) = dt

    does that help?
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  5. #4  
    Forum Professor river_rat's Avatar
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    Just a question, why is cos(t)/|cos(t)| = 1? Oh and what are the new bounds for the integral?
    As is often the case with technical subjects we are presented with an unfortunate choice: an explanation that is accurate but incomprehensible, or comprehensible but wrong.
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