Results 1 to 2 of 2

Math Help - Prove Identity

  1. #1
    Newbie
    Joined
    Jun 2005
    Posts
    10

    Prove Identity?!?!?! Please help

    How do I prove the following identities?

    sin(3pi/2 + x) = -cos x




    sin(pi/2+h)-sin(pi/2) ...cos h-1
    _________________ = ______
    ............h ....................h


    Please help I am having alot of trouble with these? Thanks
    Last edited by Math Help; July 12th 2005 at 09:10 PM.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor
    Joined
    Apr 2005
    Posts
    1,631
    Expand, expand.

    sin(3pi/2 + x) = -cos x

    Lefthand side
    = sin(3pi/2 +x)
    = sin(3pi/2)cos(x) +cos(3pi/2)sin(x)
    = (-1)cos(x) +(0)sin(x)
    = -cos(x)
    = Righthand side.

    Proven.

    ----------------------
    sin(pi/2+h)-sin(pi/2) ...cos h-1
    _________________ = ______
    ............h ....................h

    Rewriting that,
    [sin(pi/2 +h) -sin(pi/2)] / h = [cos(h) -1] / h

    Lefthand Side
    = [sin(pi/2 +h) -sin(pi/2)] / h
    = [{sin(pi/2)cos(h) +cos(pi/2)sin(h)} -(1)] / h
    = [(1)cos(h) +(0)sin(h) -1] / h
    = [cos(h) -1] / h
    = Righthand Side

    Proven
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. prove identity help!
    Posted in the Trigonometry Forum
    Replies: 7
    Last Post: December 2nd 2010, 10:00 AM
  2. prove the identity
    Posted in the Algebra Forum
    Replies: 3
    Last Post: June 7th 2010, 05:03 PM
  3. Prove this identity?
    Posted in the Trigonometry Forum
    Replies: 5
    Last Post: April 5th 2010, 05:29 PM
  4. Prove that each of the following is an identity
    Posted in the Trigonometry Forum
    Replies: 2
    Last Post: April 18th 2009, 02:39 PM
  5. Prove the Identity
    Posted in the Trigonometry Forum
    Replies: 10
    Last Post: February 25th 2008, 05:29 PM

Search Tags


/mathhelpforum @mathhelpforum