The Graphs of other Trig Functions
Sketch the graphs of y = cos(x) and y = sec(x) on the same axes.
4
3
2
1
-6.28319
-3.14159
3.14159
6.28319
-1
-2
-3
-4
Complete the following table (Don’t forget that the sec(x) = 1/cos(x) )
x-value 0
.5
.75
.9
1
1.3
1.4
1.5
1.57

2
cos(x)
sec(x)
Describe the behavior for both functions as x approaches

2
________________________________________________________________________
________________________________________________________________________
Explain how the table correlates to what you see graphically above: Be very Specific
________________________________________________________________________
Where else will similar behavior occur for the secant function? Why?
________________________________________________________________________
________________________________________________________________________
What is the period for y = sec(x)? ____________________________
Sketch the graphs of y = sin(x) and y = csc(x) on the same axes.
4
3
2
1
-6.28319 -4.71239 -3.14159 -1.5708
1.5708
3.14159 4.71239 6.28319
-1
-2
-3
-4
Complete the following table (Don’t forget that the csc(x) = 1/sin(x) )
x-value 0
.5
.75
.9
1
1.3
1.4
1.5
1.57

2
sin(x)
csc(x)
Describe the behavior for both functions as x approaches

2
________________________________________________________________________
________________________________________________________________________
Explain how the table correlates to what you see graphically above: Be very Specific
________________________________________________________________________
________________________________________________________________________
Where else will similar behavior occur for the cosecant function?
________________________________________________________________________
________________________________________________________________________
Graph y = csc(x +

)
4
4
3
2
1
-6.28319 -4.71239 -3.14159 -1.5708
1.5708
3.14159
4.71239
-1
-2
-3
-4
What do you suspect that the period of y = csc(2x) is? Verify graphically.
4
3
2
1
-6.28319 -4.71239 -3.14159
-1.5708
1.5708
-1
-2
-3
-4
Does this relate to what we did before? Explain.
3.14159
4.71239
6.28319
6.28319
Why is the study of trigonometric functions related to the study of rational functions?
Find many comparisons.
Write a summary concerning what you know concerning the graphs of trigonometric
functions. Discuss the value of such an approach from an instructional point of view and
course readings—two pages typed.