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Math Help - tangent & normal

  1. #1
    Like a stone-audioslave ADARSH's Avatar
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    Smile tangent & normal

    what's exactly a rigorous definition of
    tangent & normal to a curve suitable in all cases?

    I know its a dumb qusetion but I have problems
    in using it for concepts of calculus.
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  2. #2
    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by ADARSH View Post
    what's exactly a rigorous definition of
    tangent & normal to a curve suitable in all cases?

    I know its a dumb qusetion but I have problems
    in using it for concepts of calculus.
    the tangent line to a curve at a particular point gives the slope (rate of change) of the curve at that point. it is a straight line that touches the curve once in that vicinity. the normal line at the said point is the straight line that is perpendicular to the tangent line, and so cuts through the curve
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  3. #3
    Like a stone-audioslave ADARSH's Avatar
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    Thumbs up ...another one

    Thank you
    A line can both be tangent & normal to a curve
    but not to a function
    isn't it true.
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  4. #4
    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by ADARSH View Post
    Thank you
    A line can both be tangent & normal to a curve
    but not to a function
    isn't it true.
    um, i don't think so. by definition the normal line is perpendicular to the tangent line. they can't be one and the same line
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  5. #5
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    Tangent and Normal

    Hello ADARSH
    Quote Originally Posted by ADARSH View Post
    Thank you
    A line can both be tangent & normal to a curve
    but not to a function
    isn't it true.

    In fact, there's nothing to stop a line being both a tangent and a normal to the same curve: it could be the tangent at one point, and normal to the curve at another point.

    But perhaps that's not what you meant. So see the attachment, which shows the graph of the curve whose equation in polar coordinates is r =\sin 2 \theta. You'll see that each axis is both a tangent and a normal to the curve at the origin.

    I'm not quite sure what you mean by
    not to a function
    This curve has a straightforward function that defines it.

    Grandad
    Attached Thumbnails Attached Thumbnails tangent & normal-untitled.jpg  
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  6. #6
    Like a stone-audioslave ADARSH's Avatar
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    Well a function has only one value of y defined for any "x" but a curve as in your attatchment can have many "y" for a single "x"
    So I wanted to ask ,will that happen in both the cases which I don't think it will
    -Adarsh
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  7. #7
    MHF Contributor
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    Tangent and Normal

    Hello ADARSH
    Quote Originally Posted by ADARSH View Post
    Well a function has only one value of y defined for any "x" but a curve as in your attatchment can have many "y" for a single "x"
    So I wanted to ask ,will that happen in both the cases which I don't think it will
    -Adarsh
    I see what you mean. I think you are right. If, for a given x, there is at most one value of y, there will be only (at most) one gradient of the curve at any given point. Hence a single line cannot be both a tangent and a normal to such a curve at the same point.

    Grandad
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  8. #8
    Like a stone-audioslave ADARSH's Avatar
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    Smile yep

    Yes that's what I meant,thank you for that
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