1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Homework Help: Laplace-table cos^2

  1. Dec 9, 2004 #1
    Does anyone know how to convert

    [tex]cos^2 (2t)[/tex]

    into a form that I can use the Laplace-table on...?
  2. jcsd
  3. Dec 9, 2004 #2


    User Avatar
    Science Advisor
    Homework Helper

    How about using some trig identities:

    [tex]\cos^2 2x = \frac {1 + \cos 4x}{2}[/tex]
  4. Dec 9, 2004 #3
    Hey thanks Tide! Just one thing, I wasn't really able to find this identity anywhere in my books, and I'm not really at a level where I can come up with such identities on my own if it goes beyond turning equations around. This identity is not one of the most used is it?
  5. Dec 9, 2004 #4


    User Avatar
    Science Advisor
    Homework Helper


    It's just a variant of the sum formula which is very commonly used:

    [tex]\cos a + b = \cos a \cos b - \sin a \sin b[/tex]

    so that when a = b

    [tex]\cos 2a = \cos^2 a - \sin^2 a[/tex]

    and since

    [tex]\sin^2 a + \cos^2 a = 1[/tex]

    the identity becomes

    [tex]\cos 2a = 2 \cos^2 a - 1[/tex]

    from which

    [tex]\cos^2 a = \frac {1 + \cos 2a}{2}[/tex]

    Finally, just set a = 2x for your problem.
  6. Dec 9, 2004 #5


    User Avatar
    Staff Emeritus
    Science Advisor

Share this great discussion with others via Reddit, Google+, Twitter, or Facebook