Results 1 to 2 of 2

Thread: Parametric Equations Horzontal Tangents

  1. #1
    Mar 2008

    Parametric Equations Horzontal Tangents

    I have a question that is confusing me.

    Suppose the curve is traced by the parametric equations:
    x = 3sin(t)
    y = 25-6cos^2(t)-12sin(t)
    At what point (x,y) on this curve is the tangent line horizontal??

    I know that I need to find (dy/dt)/(dx/dt)
    I think that the derivative of y is messing me up to start with.
    Then I know I need to find the points for t and sub them into the x and y equations given but I am not getting the correct answers.
    Can anyone help?
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Moo is offline
    A Cute Angle Moo's Avatar
    Mar 2008
    P(I'm here)=1/3, P(I'm there)=t+1/3

    A tangent line is horizontal when the derivative is 0 (the derivate number is the slope of the tangent).

    So you have to solve for t as you said.

    For the derivative of y, let's do it slightly :

    $\displaystyle y = 25-6\cos^2(t)-12\sin(t)$

    We know that :

    - $\displaystyle (u+v)'=u'+v'$

    - the derivative of a constant is 0.

    - $\displaystyle \forall \lambda \in \mathbb{R}, \ (\lambda u(x))'=\lambda u'(x)$

    - $\displaystyle (u^n(x))'=n \ u'(x) \ u^{n-1}(x)$ or here, what's going to interest you is : $\displaystyle (u^2(x))'=2u'(x)u(x)$

    - the derivate of cos is -sin and the derivate of sin is cos

    I think you got all you need here =)
    If you still have difficulties show where there is a problem
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Equations of all tangents..
    Posted in the Calculus Forum
    Replies: 12
    Last Post: Nov 23rd 2010, 05:07 PM
  2. Parametric tangents and normals
    Posted in the Geometry Forum
    Replies: 2
    Last Post: Mar 27th 2010, 04:09 PM
  3. Replies: 1
    Last Post: Nov 15th 2009, 01:03 PM
  4. Tangents to Parametric Curves
    Posted in the Calculus Forum
    Replies: 1
    Last Post: Mar 22nd 2009, 04:48 PM
  5. Tangents - Parametric Equations
    Posted in the Calculus Forum
    Replies: 4
    Last Post: Mar 26th 2008, 03:55 PM

Search Tags

/mathhelpforum @mathhelpforum