Results 1 to 5 of 5

Math Help - Derivative Question

  1. #1
    Newbie
    Joined
    May 2008
    Posts
    3

    Derivative Question

    A line passes through the point (-root3, -pi/6) and is tangent to the graph y=sinx at a point for which x is an element of [0. pi/2] detirmine the slope of the tangent.

    root is a square root,

    I really dont know where to go with this
    any help would be great
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Behold, the power of SARDINES!
    TheEmptySet's Avatar
    Joined
    Feb 2008
    From
    Yuma, AZ, USA
    Posts
    3,764
    Thanks
    78
    Quote Originally Posted by tribar View Post
    A line passes through the point (-root3, -pi/6) and is tangent to the graph y=sinx at a point for which x is an element of [0. pi/2] detirmine the slope of the tangent.

    root is a square root,

    I really dont know where to go with this
    any help would be great

    let "a" be the point in [0,\frac{\pi}{2}]

    then the point (a,f(a))=(a,\sin(a)) must also be on the tangent line.

    so we can now compute the slope using these 2 points

    m=\frac{\sin(a)+\frac{\pi}{6}}{a+\sqrt{3}}

    but we also know that the slope must be equal to the derivative evaluated at a so we get

    f'(x)=\cos(x) \to m=f'(a)=\cos(a)

    We now have a system of equations in "m" and "a"

    setting them equal gives

    \frac{\sin(a)+\frac{\pi}{6}}{a+\sqrt{3}}=\cos(a)

    as far as I know (any input we be awsome )

    this doesn't have a closed form solution(there may be another way )

    but I solved the equation numericlly with Maple and it gives

    a \approx 1.047197551 this is in radians.

    I hope this helps.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Newbie
    Joined
    May 2008
    Posts
    3
    Thanks
    thats where i was going with the eqn, and i got to where you are....


    the overall answer is supposed to be (for the eqn of the line)
    y= 1/2x -pi/6 + (root3/2)

    thanks again!
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Behold, the power of SARDINES!
    TheEmptySet's Avatar
    Joined
    Feb 2008
    From
    Yuma, AZ, USA
    Posts
    3,764
    Thanks
    78
    Quote Originally Posted by tribar View Post
    Thanks
    thats where i was going with the eqn, and i got to where you are....


    the overall answer is supposed to be (for the eqn of the line)
    y= 1/2x -pi/6 + (root3/2)

    thanks again!
    Derivative Question-capture.jpg

    Numerically we have the right slope

    \frac{\pi}{3} \approx 1.047197551

    but how they sovled without using a numerical approximation I have no Idea.
    Follow Math Help Forum on Facebook and Google+

  5. #5
    Newbie
    Joined
    May 2008
    Posts
    3
    i see what you mean, my trig/algebra skills arnt as good as they used to be


    but ill try to work through it, thus far i have it at
    pi/6 = (x + sqrt3)cosx - (1/cosx)
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Derivative question.
    Posted in the Calculus Forum
    Replies: 2
    Last Post: August 14th 2011, 11:15 PM
  2. derivative question
    Posted in the Calculus Forum
    Replies: 5
    Last Post: January 20th 2010, 10:25 PM
  3. derivative question
    Posted in the Calculus Forum
    Replies: 1
    Last Post: November 16th 2009, 10:54 PM
  4. Replies: 19
    Last Post: October 19th 2009, 06:10 PM
  5. derivative question
    Posted in the Calculus Forum
    Replies: 1
    Last Post: September 30th 2007, 06:23 PM

Search Tags


/mathhelpforum @mathhelpforum