Results 1 to 4 of 4

Math Help - express cos (x - y)

  1. #1
    Junior Member
    Joined
    Dec 2005
    Posts
    40

    express cos (x - y)

    Could anyone give me some hints? I can't think the first step~


    Given that \sin x + \ sin y = a,

    \cos x + \ cos y = b,

    express the following in therms of a and b:

    (a) cos (x - y)

    (b) sin (x - y)
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Global Moderator

    Joined
    Nov 2005
    From
    New York City
    Posts
    10,616
    Thanks
    9
    Quote Originally Posted by ling_c_0202
    Could anyone give me some hints? I can't think the first step~


    Given that \sin x + \ sin y = a,

    \cos x + \ cos y = b,

    express the following in therms of a and b:

    (a) cos (x - y)

    (b) sin (x - y)
    (a)
    a=\sin x+\sin y
    Thus,
    a^2=\sin^2x+\sin^2y+2\sin x\sin y
    Thus,
    b^2=\cos^2x+\cos^2y+2\cos x\cos y
    Thus,
    a^2+b^2=\sin^2x+\cos^2x+\sin^2y+ \cos^2y+2\sin x\sin y+2\cos x\cos y
    Thus,
    a^2+b^2=1+1+2(\cos x\cos y+\sin x\sin y)
    Thus,
    \frac{a^2+b^2}{2}-1=\cos(x-y)
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Senior Member
    Joined
    Jun 2005
    Posts
    295
    Awards
    1
    Try multiplying each relation by \sqrt{\frac12} and adding and subtracting.
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Junior Member
    Joined
    Dec 2005
    Posts
    40
    Thank you very much!! ^^
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Express 2x^2-28x+53
    Posted in the Algebra Forum
    Replies: 7
    Last Post: May 16th 2011, 05:27 AM
  2. Different way to express this set
    Posted in the Discrete Math Forum
    Replies: 2
    Last Post: February 21st 2011, 11:46 AM
  3. express in m and n
    Posted in the Trigonometry Forum
    Replies: 5
    Last Post: July 22nd 2010, 09:15 PM
  4. express in z=a+bi
    Posted in the Calculus Forum
    Replies: 1
    Last Post: April 14th 2009, 11:52 PM
  5. way to express ans
    Posted in the Trigonometry Forum
    Replies: 8
    Last Post: April 17th 2006, 07:00 AM

Search Tags


/mathhelpforum @mathhelpforum