Results 1 to 5 of 5

Math Help - trig identities

  1. #1
    Newbie
    Joined
    Jul 2010
    Posts
    9

    trig identities

    I’m stuck on the following problem (see Attachment) any help would be greatly appreciated

    trig identities 2.rtf


    I’m not sure how it goes from here to the next line
    Thanks
    Kind regards
    Last edited by JCM133; August 9th 2010 at 03:03 PM.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor
    skeeter's Avatar
    Joined
    Jun 2008
    From
    North Texas
    Posts
    11,702
    Thanks
    454
    you need to review your post ...
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Newbie
    Joined
    Jul 2010
    Posts
    9

    Trigonometric Identities

    Hi All
    Im having a problem with the problem in the attached file

    trig identities 2.rtf

    any help would be greatly appreciated
    Thanks Kind Regards

    John
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Senior Member eumyang's Avatar
    Joined
    Jan 2010
    Posts
    278
    Thanks
    1
    2 \left( \sin \frac{\theta}{2} \cos \frac{\theta}{2} \cos^2  \frac{\phi}{2} + \sin \frac{\phi}{2} \cos \frac{\phi}{2} \cos^2  \frac{\theta}{2} + \sin \frac{\phi}{2} \cos \frac{\phi}{2} \sin^2  \frac{\theta}{2} + \sin \frac{\theta}{2} \cos \frac{\theta}{2} \sin^2  \frac{\phi}{2}\right)
    (I rearranged the factors in the last term to make it consistent.)


    Distribute the 2:
    2 \sin \frac{\theta}{2} \cos \frac{\theta}{2} \cos^2  \frac{\phi}{2} + 2 \sin \frac{\phi}{2} \cos \frac{\phi}{2} \cos^2  \frac{\theta}{2} + 2 \sin \frac{\phi}{2} \cos \frac{\phi}{2} \sin^2  \frac{\theta}{2} + 2 \sin \frac{\theta}{2} \cos \frac{\theta}{2} \sin^2  \frac{\phi}{2}


    Note that each term begins with 2\sin \frac{\theta}{2} \cos \frac{\theta}{2} or 2\sin \frac{\phi}{2} \cos \frac{\phi}{2}. Recall the sine of a double angle identity: \sin 2u = 2\sin u \cos u So
    2\sin \frac{\theta}{2} \cos \frac{\theta}{2} = \sin \left( 2\cdot \frac{\theta}{2} \right) = \sin \theta, and the same for angle phi.


    Replace:
    \sin \theta \cos^2  \frac{\phi}{2} + \sin \phi \cos^2  \frac{\theta}{2} + \sin \phi \sin^2  \frac{\theta}{2} + \sin \theta \sin^2  \frac{\phi}{2}


    Rearrange:
    \sin \theta \cos^2  \frac{\phi}{2} + \sin \theta \sin^2  \frac{\phi}{2} + \sin \phi \cos^2  \frac{\theta}{2} + \sin \phi \sin^2  \frac{\theta}{2}


    Factor:
    \sin \theta \left( \cos^2  \frac{\phi}{2} + \sin^2  \frac{\phi}{2} \right) + \sin \phi \left( \cos^2  \frac{\theta}{2} + \sin^2  \frac{\theta}{2} \right)


    Use the Pythagorean identity:
    \sin \theta (1) + \sin \phi (1)

    \sin \theta + \sin \phi
    Follow Math Help Forum on Facebook and Google+

  5. #5
    Newbie
    Joined
    Jul 2010
    Posts
    9
    Thanks EUMYANG that has helped a bundle

    kind regards
    John
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. trig identities
    Posted in the Trigonometry Forum
    Replies: 1
    Last Post: November 13th 2009, 01:37 PM
  2. Trig identities
    Posted in the Trigonometry Forum
    Replies: 2
    Last Post: September 30th 2009, 05:40 PM
  3. Trig Identities
    Posted in the Trigonometry Forum
    Replies: 2
    Last Post: January 24th 2009, 01:45 PM
  4. identities (trig)
    Posted in the Calculus Forum
    Replies: 2
    Last Post: September 30th 2008, 09:58 AM
  5. Trig identities
    Posted in the Trigonometry Forum
    Replies: 4
    Last Post: September 28th 2008, 03:36 PM

Search Tags


/mathhelpforum @mathhelpforum