tangent & normal

Printable View

October 21st 2008, 06:12 AM
ADARSH

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.
October 21st 2008, 07:09 AM
Jhevon

Quote:

Originally Posted by ADARSH

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
October 22nd 2008, 03:52 AM
ADARSH

...another one

Thank you
A line can both be tangent & normal to a curve
but not to a function
isn't it true. (Angel)
January 17th 2009, 04:23 PM
Jhevon

Quote:

Originally Posted by ADARSH

Thank you
A line can both be tangent & normal to a curve
but not to a function
isn't it true. (Angel)

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
January 17th 2009, 10:39 PM
Grandad

1 Attachment(s)

Tangent and Normal

Hello ADARSH

Quote:

Originally Posted by ADARSH

Thank you
A line can both be tangent & normal to a curve
but not to a function
isn't it true. (Angel)

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

Quote:

not to a function

This curve has a straightforward function that defines it.

Grandad
January 17th 2009, 10:48 PM
ADARSH

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" (Nod)
So I wanted to ask ,will that happen in both the cases which I don't think it will(Shake)
-Adarsh
January 17th 2009, 11:07 PM
Grandad

Tangent and Normal

Hello ADARSH

Quote:

Originally Posted by ADARSH

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" (Nod)
So I wanted to ask ,will that happen in both the cases which I don't think it will(Shake)
-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
January 18th 2009, 03:00 AM
ADARSH

yep

Yes that's what I meant,thank you for that(Happy)