Results 1 to 3 of 3

Math Help - Derivative of trig function to equal zero.

  1. #1
    Junior Member
    Joined
    Jan 2013
    From
    australia
    Posts
    39

    Derivative of trig function to equal zero.

    Hi, everyone,

    I have the trig function g(x)=cos^4(x)-cos^2(x) and i have found g'(x) to be -4sin(x)cos^3(x)+2sin(x)cos(x). how would i find when the derivative is equal to zero? I started to rearrange it to see if that would help but now i am stuck.

    2sin(x)cos(x)=sin(2x) and,

    -4sin(x)cos^3(x)=-4((1/2)sin(2x))cos^2(x)=-2sin(2x)cos^2(x).

    Any ideas?

    Thanks
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor
    Joined
    Sep 2012
    From
    Australia
    Posts
    3,648
    Thanks
    601

    Re: Derivative of trig function to equal zero.

    Hey mcleja.

    Hint: Try dividing both sides by sin(2x) and simplify.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Super Member
    Joined
    Jul 2012
    From
    INDIA
    Posts
    829
    Thanks
    209

    Re: Derivative of trig function to equal zero.

    Put g(x) = 0, we get
    2cosx sinx 4cos^3xsinx = 0
    2cosx sinx [ 1 2 cos^2x] = 0
    Cos x = 0 gives x = π/2 + nπ
    Sinx = 0 gives x = nπ
    [ 1 2 cos^2x] = 0 gives cos x = 1/√2 that will give x = nπ π/4
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Replies: 4
    Last Post: October 17th 2012, 06:51 AM
  2. derivative of trig function
    Posted in the Calculus Forum
    Replies: 4
    Last Post: February 10th 2011, 12:18 PM
  3. Derivative of a trig function
    Posted in the Calculus Forum
    Replies: 2
    Last Post: July 20th 2010, 11:24 AM
  4. Replies: 4
    Last Post: November 5th 2009, 12:53 PM
  5. Derivative of Trig Function
    Posted in the Calculus Forum
    Replies: 4
    Last Post: September 28th 2008, 03:32 PM

Search Tags


/mathhelpforum @mathhelpforum