Drexel dragonThe Math ForumDonate to the Math Forum

Ask Dr. Math - Questions and Answers from our Archives
_____________________________________________
Associated Topics || Dr. Math Home || Search Dr. Math
_____________________________________________

Trigonometry in the Third Dimension


Date: 04/30/98 at 07:45:23
From: Brett W.
Subject: What does working in 3D change?

Hi,

I'm trying to figure out an extremely trivial calculus problem that 
deals in three dimensions. If I want to use trigonometry or calculus 
in 3D, does it change much? Do I have to use those functions a special 
way? I've tried just guessing but you can define an angle three 
different ways in 3D (ratio of x to y, x to z and y to z). Am I on the 
wrong track?

Thanks,
Brett W.


Date: 04/30/98 at 08:21:00
From: Doctor Jerry
Subject: Re: What does working in 3D change?

Hi Brett,

Using trigonometry in R^3 doesn't change in principle, but it is 
somewhat harder to visualize. Mostly, trig enters through vectors.  
Most of trigonometry is captured in the idea of vector and the dot and 
cross products.

To define an angle, you need more context. The angle between two 
lines that intersect is not hard to find. If you give the lines in 
vector form:

     line 1: r = a+t*b, -oo < t < oo

     line 2: r = p+s*q, -oo < s < oo

where a, b, p, and q are vectors and t and s are parmeters, the angle 
w between these lines can be calculated from:

                 b.q
     cos(w) = ---------
              (|b|*|q|)

Note, the period represents the dot-product.

The angle between planes is calculated by looking at the angle between 
vectors normal to the planes.

The angle between two curves that meet at a point is calculated by 
calculating the angle between their tangent vectors.

-Doctor Jerry,  The Math Forum
Check out our web site! http://mathforum.org/dr.math/   
    
Associated Topics:
High School Geometry
High School Higher-Dimensional Geometry

Search the Dr. Math Library:


Find items containing (put spaces between keywords):
 
Click only once for faster results:

[ Choose "whole words" when searching for a word like age.]

all keywords, in any order at least one, that exact phrase
parts of words whole words

Submit your own question to Dr. Math

[Privacy Policy] [Terms of Use]

_____________________________________
Math Forum Home || Math Library || Quick Reference || Math Forum Search
_____________________________________

Ask Dr. MathTM
© 1994-2013 The Math Forum
http://mathforum.org/dr.math/