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Trig integration

  1. Oct 13, 2004 #1
    How do you integrate even powers of trig functions, such as

    [tex]\int\cos^{2}{\theta} \,d\theta[/tex]
     
  2. jcsd
  3. Oct 13, 2004 #2

    phy

    User Avatar

    Just an idea: perhaps you could break the integral into cos(theta)*cos(theta) and then integrate by parts from there :smile:
     
  4. Oct 14, 2004 #3
    tandoorichciken, you must use an identity

    [tex]

    cos^2 \theta = \frac{1 + cos 2\theta}{2}

    [/tex]

    When the cosine function is raised to an even integer, say for example 4,

    [tex]
    cos^4 \theta = (cos^2)^2 = (\frac{1 + cos 2\theta}{2})^2
    [/tex]

    For the sine function, use the identity

    [tex]

    sin^2 \theta = \frac{1 - cos 2\theta}{2}

    [/tex]

    A word of Caution. When doing this method do not forget to double your angle ^_^
     
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