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What is the difference between a normal line and a tangent line?

  1. Apr 11, 2007 #1
    What is the difference between a normal line and a tangent line?
     
  2. jcsd
  3. Apr 12, 2007 #2

    Tom Mattson

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    A line is tangent to a curve if:

    1. They both meet at some point.
    2. They both have the same slope at that point.

    A line is normal to a curve if:

    1. They both meet at some point.
    2. They are perpendicular to each other at that point.
     
  4. Apr 12, 2007 #3
    Addendum to 1: They meet at only one point.
     
  5. Apr 12, 2007 #4

    Not quite. The line [itex]y=1[/itex] is tangent to the curve [itex]y=\sin{x}[/itex], but they intersect each other at infinitely many points!
     
    Last edited: Apr 12, 2007
  6. Apr 12, 2007 #5
    Yes, you're right.

    Then, I guess someone needs to correct this Mathworld article
     
  7. Apr 12, 2007 #6
    Yes, they do! The article on "tangent line" gets it right, however :wink:.
     
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