Results 1 to 3 of 3

Math Help - Show this curve has 2 tangents at (0,0)

  1. #1
    Junior Member
    Joined
    Nov 2007
    Posts
    41

    Show this curve has 2 tangents at (0,0)

    Hey, this is my final question for my assignment. Needless to say, i'm stuck.

    Use the given curve to answer the following questions.
    x = 3cos(t)
    y = sin(t)cos(t)

    (a)Show that this curve has two tangents at (0, 0) and find their equations.
    y=? (smaller slope)
    y=? (larger slope)

    i did this:
    dy/dx = (dy/dt)/(dx/dt) = ((cost)^2 - (sint)^2)/-3sint
    so since i know it's at (0,0), i know that i have to sub t=0, but if i do that then the slope becomes undefined. so i dont know what i'm doing wrong here. I appreciate any help, thanks.

    ps. i want to thank everyone for helping me tonight with my assignment, and sorry for not writing it in that fancy math code, i dont know how to do trig that way.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    is up to his old tricks again! Jhevon's Avatar
    Joined
    Feb 2007
    From
    New York, USA
    Posts
    11,663
    Thanks
    3
    Quote Originally Posted by CenturionMonkey View Post
    Hey, this is my final question for my assignment. Needless to say, i'm stuck.

    Use the given curve to answer the following questions.
    x = 3cos(t)
    y = sin(t)cos(t)

    (a)Show that this curve has two tangents at (0, 0) and find their equations.
    y=? (smaller slope)
    y=? (larger slope)

    i did this:
    dy/dx = (dy/dt)/(dx/dt) = ((cost)^2 - (sint)^2)/-3sint
    so since i know it's at (0,0), i know that i have to sub t=0, but if i do that then the slope becomes undefined. so i dont know what i'm doing wrong here. I appreciate any help, thanks.

    ps. i want to thank everyone for helping me tonight with my assignment, and sorry for not writing it in that fancy math code, i dont know how to do trig that way.
    no, (0,0) refers to x and y, not t. for instance, if t = 0, then x = 3, note zero. thus you would have the point (3,0), which is note what you want.

    to find the slope of the tangent line, find where dy/dx = 0, and sove
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Flow Master
    mr fantastic's Avatar
    Joined
    Dec 2007
    From
    Zeitgeist
    Posts
    16,948
    Thanks
    5
    Quote Originally Posted by CenturionMonkey View Post
    Hey, this is my final question for my assignment. Needless to say, i'm stuck.

    Use the given curve to answer the following questions.
    x = 3cos(t)
    y = sin(t)cos(t)

    (a)Show that this curve has two tangents at (0, 0) and find their equations.
    y=? (smaller slope)
    y=? (larger slope)

    i did this:
    dy/dx = (dy/dt)/(dx/dt) = ((cost)^2 - (sint)^2)/-3sint
    so since i know it's at (0,0), i know that i have to sub t=0, but if i do that then the slope becomes undefined. so i dont know what i'm doing wrong here. I appreciate any help, thanks.

    ps. i want to thank everyone for helping me tonight with my assignment, and sorry for not writing it in that fancy math code, i dont know how to do trig that way.
    The cartesian point (0, 0) corresponds to t = \frac{\pi}{2} and t = \frac{3 \pi}{2}. Now note that the value of \frac{dy}{dx} is different for these two values of t.

    I haven't looked closely but it's likely that (0, 0) is a double point, that is, a point at which the curve intersects itself. A double point is an example of a crunode.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Replies: 3
    Last Post: February 15th 2011, 02:54 PM
  2. Replies: 5
    Last Post: September 15th 2010, 08:12 AM
  3. Graphing the curve and both tangents...
    Posted in the Calculus Forum
    Replies: 4
    Last Post: August 22nd 2010, 04:06 AM
  4. Tangents to a curve
    Posted in the Calculus Forum
    Replies: 2
    Last Post: May 16th 2009, 09:58 AM
  5. tangents and normals to curve
    Posted in the Calculus Forum
    Replies: 15
    Last Post: September 29th 2008, 03:03 PM

Search Tags


/mathhelpforum @mathhelpforum