CALCULUS Understanding Its Concepts and Methods

Normal, Orthogonal, Perpendicular

Two lines are said to be normal, orthogonal, or perpendicular to one another if they cross at right angles. A line is said to be normal to a curve or to a surface if it is perpendicular to the tangent plane at the point where the line meets the curve or surface.

Two curves are orthogonal to one another at a point where they intersect if their tangent lines at that point are orthogonal to one another.

Two functions
*f*(*x*)
and
*g*(*x*)
are orthogonal to one another on
[-p,p]
if
.

This has nothing to do with whether the graphs of
*f*
and
*g*
intersect at right angles. In fact, any two of the functions that make up
trigonometric polynomials,
1,
cos *x*,
sin *x*,
cos 2*x*,
sin 2*x*,
cos 3*x*,
sin 3*x*,
,
are orthogonal.

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Copyright © 2006 Darel Hardy, Fred Richman, Carol Walker, Robert Wisner. All rights reserved. Except upon the express prior permission in writing, from the authors, no part of this work may be reproduced, transcribed, stored electronically, or transmitted in any form by any method.