Results 1 to 4 of 4

Math Help - intersection of graphs

  1. #1
    Senior Member
    Joined
    Oct 2009
    Posts
    459

    intersection of graphs

    I need to find the points of intersection of sin 2x and sin 4x in degrees. I can do this kind of question but this one is difficult.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    -1
    e^(i*pi)'s Avatar
    Joined
    Feb 2009
    From
    West Midlands, England
    Posts
    3,053
    Thanks
    1
    Quote Originally Posted by Stuck Man View Post
    I need to find the points of intersection of sin 2x and sin 4x in degrees. I can do this kind of question but this one is difficult.
    Use the identities for sin(4x) and sin(2x)

    \sin(4x) = 4\sin(x) \cos^3(x) - 4\sin^3(x) \cos(x) = 4\sin(x) \cos(x)(\cos^2(x)-\sin^2(x))

    \sin(2x)  = 2 \sin(x) \cos(x)


    4\sin(x) \cos(x)(\cos^2(x)-\sin^2(x)) = 2 \sin(x) \cos(x)

    4\sin(x) \cos(x)(\cos^2(x)-\sin^2(x)) - 2 \sin(x) \cos(x) = 0

    [2 \sin(x) \cos(x)][2cos(2x)+1] = 0

    Either \sin(x) = 0, \cos(x) = 0 or 2\cos(2x)+1 = 0
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Senior Member
    Joined
    Oct 2009
    Posts
    459
    Identities of sin 4x aren't part of my course so I should be using the ones usually learned earlier. I can use sin 2x and cos 2x.
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Senior Member
    Joined
    Oct 2009
    Posts
    459
    I have done it using sin 4x = sin(2x + 2x). It was particularly hard compared to previous questions in the book.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Equation for Intersection Points of Graphs
    Posted in the Trigonometry Forum
    Replies: 3
    Last Post: June 7th 2011, 08:19 AM
  2. Newtons method. Intersection between graphs.
    Posted in the Calculus Forum
    Replies: 5
    Last Post: April 13th 2011, 12:49 PM
  3. Replies: 3
    Last Post: March 20th 2011, 10:40 AM
  4. Finding the intersection between two graphs
    Posted in the Calculus Forum
    Replies: 2
    Last Post: March 2nd 2010, 06:31 AM
  5. Graphs/equations/point of intersection
    Posted in the Pre-Calculus Forum
    Replies: 3
    Last Post: May 18th 2009, 05:03 PM

Search Tags


/mathhelpforum @mathhelpforum