Showing posts with label evens. Show all posts
Showing posts with label evens. Show all posts

Tuesday, January 17, 2012

Even and Odd Intervals

The following are a few student observations about graphing the secant and cosecent functions:

Re:  Secant/Cosecant Graphs-

The graphs of co-secant and secant graphs are both similar and different. 
1.       A co-secant graph is a shift of 90 degrees or pi/2 to the right of a secant graph. 
2.       The asymptotes for a secant graph cut through the center of the parabolic-structure of co-secant graphs. 
3.       The asymptotes for co-secant graphs cut through the center of a secant graph.
4.       When a sine graph's x-value is zero, the x-value for a secant graph is also zero. 
5.       When the x-value for a cosine graph is zero, the x-value of a co-secant graph is also zero. 
6.       All odd intervals of pi have the secant graphs opening downward. 
7.       All odd intervals of 3pi/2 have co-secant graphs opening downward. 
8.       All even intervals of pi have secant graphs opening upwards. 
9.       All even intervals of  3pi/2 have co-secant graphs opening upwards
Question:  Is there an algebraic way of modeling

"all odd intervals of"

"all even intervals of"

Hint:  It may involve k's and Z's

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