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
6.28319
-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
3.14159
4.71239
6.28319
-1
-2
-3
-4
Does this relate to what we did before? Explain.
Why is the study of trigonometric functions related to the study of rational functions?
Find many comparisons.