Results 1 to 4 of 4

Math Help - Help with trig proofs.

  1. #1
    Newbie
    Joined
    Apr 2007
    Posts
    7

    Help with trig proofs. [edit: one remaining]

    I'm stumped on three problems that were assigned on a math project for Algebra II/Trig.

    [SOLVED] 1) Express the following function as a single circular sinusoid.
    f(x)=sqrt(3)*sin(2x)+cos(2x)

    2) Prove that if y1=a1*sin(bx) and y2=a2*cos(bx), then A is an element of the real number and B is an element of the real number such that a1*sin(bx)+a2*cos(bx)=Asin(k(x+B)). A should be in terms of a1 and a2, and there should be only one expression for B. Also, state what the constant k is equal to.

    [SOLVED, YAY!] 3) Prove that:
    (1/2)+cos(x)+cos(2x)+cos(3x)......+cos(nx)=

    sin((n+1/2)x)
    ---------------
    2sin(x/2)

    I apologize for the bad formatting (don't know how to get MathType into the forum. )

    Any help would be greatly appreciated.
    Last edited by mad_munky838; April 9th 2007 at 07:14 PM.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Super Member

    Joined
    May 2006
    From
    Lexington, MA (USA)
    Posts
    11,749
    Thanks
    649
    Hello, mad_munky838!

    I can help you with the first one.
    . . The solution is a strange one . . .


    1) Express the following function as a single circular sinusoid:
    . . f(x) .= .√3·sin(2x) + cos(2x)

    Divide both sides by 2:

    . . ˝·f(x) .= .˝·√3·sin(2x) + ˝·cos(2x)

    We know that: .cos(30°) = ˝√3 .and .sin(30°) = ˝

    So we have: .˝·f(x) .= .cos(30°)·sin(2x) + sin(30°)·cos(2x)

    . . . . . - . . . - . . . . .= .sin(2x)·cos(30°) + cos(2x)·sin(30°)


    From the compound-angle identity: .sin(A + B) .= .sin(A)·cos(B) + cos(A)·sin(B)

    . . we have: .˝·f(x) .= .sin(2x + 30°)


    Therefore: .f(x) .= .2·sin(2x + 30°)

    Follow Math Help Forum on Facebook and Google+

  3. #3
    Global Moderator

    Joined
    Nov 2005
    From
    New York City
    Posts
    10,616
    Thanks
    9
    Quote Originally Posted by mad_munky838 View Post

    3) Prove that:
    (1/2)+cos(x)+cos(2x)+cos(3x)......+cos(nx)=

    sin((n+1/2)x)
    ---------------
    2sin(x/2)

    I apologize for the bad formatting (don't know how to get MathType into the forum. )

    Any help would be greatly appreciated.
    This is not true.

    Try n=1.
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Newbie
    Joined
    Apr 2007
    Posts
    7
    Thanks for the help!

    @Soroban:
    The solution is a strange one . . .
    my teacher adores tricky/strange problems... It's extremely frustrating for us, the students.
    Thanks for the answer, been staring at it and trying to work out something for a long time. Would've never thought of dividing both sides by 2.

    @ThePerfectHacker: I did try n=1, and graphing it, it's the same:
    y1= (1/2) + cos(x)
    y2=sin((1+1/2)x)/(2sin(x/2))
    both give same graph. Of course, y2 doesn't work when 2sin(x/2)=0. But otherwise, it worked =/.

    EDIT: SOLVED, just #2 remaining
    Last edited by mad_munky838; April 6th 2007 at 05:45 PM.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. two trig proofs
    Posted in the Trigonometry Forum
    Replies: 1
    Last Post: April 3rd 2011, 01:21 AM
  2. trig proofs
    Posted in the Trigonometry Forum
    Replies: 1
    Last Post: May 23rd 2010, 07:08 PM
  3. Trig proofs help!
    Posted in the Trigonometry Forum
    Replies: 7
    Last Post: December 13th 2009, 11:34 PM
  4. Trig Proofs
    Posted in the Trigonometry Forum
    Replies: 0
    Last Post: March 29th 2009, 06:55 AM
  5. trig proofs
    Posted in the Trigonometry Forum
    Replies: 5
    Last Post: November 11th 2008, 07:48 AM

Search Tags


/mathhelpforum @mathhelpforum