Using Graphs of Trigonometric Functions

Date: 10/9/95 at 23:31:27
From: Anonymous
Subject: applications of csc, sec, and cot graphs

In class, we are working on csc, sec, and cot graphs, including how to 
change the sin, cos, and tan graphs to get them.  I don't have a problem 
calculating and expressing the graphs themselves, but I am interested
in applications of these graphs.  For example: in what field would it
be useful to know the period, the location of the asymptotes, and the 
domain of a sec graph?

Thanks

Date: 11/5/95 at 16:36:48
From: Doctor Rob
Subject: Re: applications of csc, sec, and cot graphs

Hi.  

The reciprocal trigonometric functions are important and applicable 
because they, like the other trigonometric functions, are 
periodic, and many situations arise in the natural and social 
sciences that can be modeled with these periodic functions. 
Granted, the Sin, Cos, and Tan functions are most commonly used in 
direct modeling, but the reciprocal functions often arise when you 
do calculus on these functions.  For example, Integral (tan x) = 
1/sec^2 x. Understanding the basic properties of these reciprocal 
functions - period, asymptotes, domain, range, etc. - is key if 
you're to use them in models. Graphs help some people to learn  
and internalize these properties - they're learning tools.  So, in 
summary, the functions are important because they are periodic, 
and the graphs are important because they help to understand these 
functions.   

-Doctor Rob,  The Geometry Forum