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Tangent Lines

  1. Mar 29, 2009 #1
    The problem statement, all variables and given/known data[/b]
    My book talks about find the two tangent lines at the point (0,2) for http://mathbin.net/equations/7402_0.png [Broken] and http://mathbin.net/equations/7402_1.png [Broken].[/URL] It says that t then is equal to pi/2 and -pi/2. I do not know how to they solved for this t. Any help?
    Last edited by a moderator: May 4, 2017
  2. jcsd
  3. Mar 29, 2009 #2


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    You solve the simultaneous equation
    [tex]x = 0, y = 2[/tex]

    It's easiest starting with the latter:
    [tex]2 = y = 2 - \pi \cos t \implies 0 = - \pi \cos t \implies t = \pm \frac{\pi}{2}[/tex]
    and then all you have to do is plug them both into the equation for x and check that it gives zero (i.e. you have two values of t for which (0, 2) is on the curve).
  4. Mar 29, 2009 #3
    Why didn't we include [tex]\frac{ \pi }{2}+2n \pi[/tex]?

    Thank you!
  5. Mar 29, 2009 #4


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    Because there are no such points at which the curve goes through (0, 2).
    You can plug it in:
    x(pi/2 + 2 pi) = ... ?
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