Results 1 to 3 of 3

Math Help - Trig relationship

  1. #1
    Junior Member
    Joined
    Apr 2009
    Posts
    48

    Trig relationship

    I'm working through a problem set for a class unlrelated to trigonometry, but reached a dead end when I failed to recognize that

    2cos^2(x)- sin^2(x) = 3cos^2(x)-1

    Could somebody kindly show me why this is the case? (I've never actually taken a formal trigonometry class, so my background is fairly weak).

    Thanks.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor
    Prove It's Avatar
    Joined
    Aug 2008
    Posts
    11,570
    Thanks
    1428
    Quote Originally Posted by Ares_D1 View Post
    I'm working through a problem set for a class unlrelated to trigonometry, but reached a dead end when I failed to recognize that

    6 (2cos^2(x)- sin^2(x)) = 18cos^2(x)-6

    Could somebody kindly show me why this is the case? (I've never actually taken a formal trigonometry class, so my background is fairly weak).

    Thanks.
    Use the Pythagorean Identity

    \sin^2{x} + \cos^2{x} = 1

    \sin^2{x} = 1 - \cos^2{x}.


    So that means

    6(2\cos^2{x} - \sin^2{x}) = 6[2\cos^2{x} - (1 - \cos^2{x})]

     = 6(2\cos^2{x} - 1 + \cos^2{x})

     = 6(3\cos^2{x} - 1)

     = 18\cos^2{x} - 6.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Junior Member
    Joined
    Apr 2009
    Posts
    48
    Quote Originally Posted by Prove It View Post
    Use the Pythagorean Identity

    \sin^2{x} + \cos^2{x} = 1

    \sin^2{x} = 1 - \cos^2{x}.


    So that means

    6(2\cos^2{x} - \sin^2{x}) = 6[2\cos^2{x} - (1 - \cos^2{x})]

     = 6(2\cos^2{x} - 1 + \cos^2{x})

     = 6(3\cos^2{x} - 1)

     = 18\cos^2{x} - 6.
    Cheers, thanks!
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Relationship
    Posted in the Algebra Forum
    Replies: 17
    Last Post: March 1st 2010, 05:55 PM
  2. relationship help
    Posted in the Discrete Math Forum
    Replies: 11
    Last Post: October 12th 2009, 06:42 AM
  3. relationship between a,b and c
    Posted in the Calculus Forum
    Replies: 1
    Last Post: August 15th 2009, 01:37 AM
  4. Replies: 2
    Last Post: April 18th 2009, 06:27 AM
  5. Relationship between X and Y!
    Posted in the Advanced Statistics Forum
    Replies: 4
    Last Post: August 29th 2007, 02:20 PM

Search Tags


/mathhelpforum @mathhelpforum