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

1. Apr 11, 2007

mathmann

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

2. Apr 12, 2007

Tom Mattson

Staff Emeritus
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.

3. Apr 12, 2007

neutrino

Addendum to 1: They meet at only one point.

4. Apr 12, 2007

Data

Not quite. The line $y=1$ is tangent to the curve $y=\sin{x}$, but they intersect each other at infinitely many points!

Last edited: Apr 12, 2007
5. Apr 12, 2007

neutrino

Yes, you're right.

Then, I guess someone needs to correct this Mathworld article

6. Apr 12, 2007

Data

Yes, they do! The article on "tangent line" gets it right, however .