Results 1 to 2 of 2

Math Help - trig identity

  1. #1
    Junior Member
    Joined
    Mar 2009
    From
    west sussex
    Posts
    31

    trig identity

    hi

    have this function g(x)=cos(x)exp(2/3sin(x)) 0<x<2pie

    also have derivative g'(x)=1/3(2-3sinx-2sin^2x)(exp2/3sinx)

    i need to find the stationary points of g(x) and classify each point min and max. the domain is [0,2pie]

    my main problem is i do not know how to get any values to use in original function i am not sure about trig identity. i am sure that i need to set 1/3(2-3sinx-2sin^2x) to 0 but thats as far i as go.

    any help would be great
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Super Member redsoxfan325's Avatar
    Joined
    Feb 2009
    From
    Swampscott, MA
    Posts
    943
    Quote Originally Posted by smartcar29 View Post
    hi

    have this function g(x)=cos(x)exp(2/3sin(x)) 0<x<2pie

    also have derivative g'(x)=1/3(2-3sinx-2sin^2x)(exp2/3sinx)

    i need to find the stationary points of g(x) and classify each point min and max. the domain is [0,2pie]

    my main problem is i do not know how to get any values to use in original function i am not sure about trig identity. i am sure that i need to set 1/3(2-3sinx-2sin^2x) to 0 but thats as far i as go.

    any help would be great
    Don't worry about the \frac{1}{3}; it's just a constant multiple. To solve 2-3\sin x-2\sin^2x=0, just treat \sin x like you would x and factor it.

    We know that 2-3x-2x^2 factors into (1-2x)(2+x), so 2-3\sin x-2\sin^2x factors into (1-2\sin x)(2+\sin x). Then set each part equal to 0.

    Spoiler:
    1-2\sin x=0 \implies \sin x =\frac{1}{2} \implies x = \frac{\pi}{6} or \frac{5\pi}{6}

    2+\sin x=0 \implies \sin x=-2 which has no solutions.

    So at x=\frac{\pi}{6} and x=\frac{5\pi}{6}, g'(x)=0.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. trig identity help.
    Posted in the Trigonometry Forum
    Replies: 3
    Last Post: December 6th 2009, 01:19 PM
  2. yet another trig identity...
    Posted in the Trigonometry Forum
    Replies: 3
    Last Post: May 27th 2009, 11:59 AM
  3. trig identity
    Posted in the Trigonometry Forum
    Replies: 3
    Last Post: May 25th 2009, 10:44 AM
  4. Trig Identity
    Posted in the Trigonometry Forum
    Replies: 7
    Last Post: January 22nd 2009, 02:16 PM
  5. Trig Identity Help
    Posted in the Trigonometry Forum
    Replies: 3
    Last Post: January 20th 2009, 08:56 PM

Search Tags


/mathhelpforum @mathhelpforum