Results 1 to 2 of 2

Math Help - Word Problem - derivatives in trig functions

  1. #1
    Junior Member
    Joined
    Sep 2009
    Posts
    32

    Word Problem - derivatives in trig functions

    In a Calculus problem, I found the rate of change of F with respect to x, resulting in:

    dF/dx = -(uW)(ucos(x) - sin(x)) / (usin(x) + cos(x))^2

    where u and W are coefficients. The problem then asks me to find when the rate of change is equal to 0, and it seems to indicate that I should find the equation that x is equal to.

    How would I go about figuring out what x is? And in general, when there is a trigonometric function and I need to find x, how would I pull that variable out of the equation?

    Another question involving the problem: If W = 70 and u = .7, how would I draw the graph of F [F = uW / (usin(x) + cos(x))]as a function of x and use it to find the value of x for which dF/dx = 0?

    I plugged in the equation [y = 49/(.7sin(X) + cos(x)]into my graphing calculator and got the function. There was a curve like x^2 with the minimum at 34.992, so I thought that would be where where the derivative would equal 0, since there would be a horizontal tangent line there. However, Webassign said x = 34.992 was wrong. What am I doing wrong? And other than using the graphing calculator, is there another way to find x?

    Thanks.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor
    skeeter's Avatar
    Joined
    Jun 2008
    From
    North Texas
    Posts
    11,741
    Thanks
    481
    Quote Originally Posted by Maziana View Post
    In a Calculus problem, I found the rate of change of F with respect to x, resulting in:

    dF/dx = -(uW)(ucos(x) - sin(x)) / (usin(x) + cos(x))^2

    where u and W are coefficients. The problem then asks me to find when the rate of change is equal to 0, and it seems to indicate that I should find the equation that x is equal to.

    How would I go about figuring out what x is? And in general, when there is a trigonometric function and I need to find x, how would I pull that variable out of the equation?

    \textcolor{red}{u\cos{x} - \sin{x} = 0}

    \textcolor{red}{u = \tan{x}}

    \textcolor{red}{x = \arctan{u}}

    Another question involving the problem: If W = 70 and u = .7, how would I draw the graph of F [F = uW / (usin(x) + cos(x))]as a function of x and use it to find the value of x for which dF/dx = 0?

    use a calculator

    I plugged in the equation [y = 49/(.7sin(X) + cos(x)]into my graphing calculator and got the function. There was a curve like x^2 with the minimum at 34.992, so I thought that would be where where the derivative would equal 0, since there would be a horizontal tangent line there. However, Webassign said x = 34.992 was wrong. What am I doing wrong? And other than using the graphing calculator, is there another way to find x?

    ... x = 34.992 is correct. maybe a significant figure error? or maybe your original function for F is in error?

    Thanks.
    ...
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Derivatives of trig functions
    Posted in the Calculus Forum
    Replies: 4
    Last Post: November 14th 2010, 08:00 AM
  2. Derivatives of Trig functions
    Posted in the Calculus Forum
    Replies: 8
    Last Post: April 24th 2010, 08:27 AM
  3. derivatives of trig functions
    Posted in the Calculus Forum
    Replies: 1
    Last Post: October 28th 2009, 02:12 PM
  4. derivatives of trig functions
    Posted in the Calculus Forum
    Replies: 2
    Last Post: October 5th 2008, 06:40 PM
  5. Derivatives of Inv Trig Functions
    Posted in the Calculus Forum
    Replies: 3
    Last Post: March 18th 2008, 08:15 PM

Search Tags


/mathhelpforum @mathhelpforum