1. Chapter 4 Trigonometric Functions
Pre-Calculus
Chapter 4
Trigonometric Functions

2. 4.6 Graphs of Other Trigonometric Functions
Objectives:
Sketch the graphs of tangent functions.
Sketch the graphs of cotangent functions.
Sketch the graphs of secant and cosecant functions.
Sketch the graphs of damped trigonometric functions.

3. Tangent and Cotangent Complete the worksheet
“Graphs of Tangent and Cotangent”

4. Graph of Tangent
Domain:
Range:
Period:
Zeros:
Vertical Asymptotes:

5. Graph of Cotangent
Domain:
Range:
Period:
Zeros:
Vertical Asymptotes:

6. General Form of Tangent and Cotangent
The general form of tangent and cotangent are: y = a tan (bx – c)
y = a cot (bx – c)
Where
π/b = period
c = horizontal shift

7. Graph Transformation of Tangent
To sketch the graph of y = a tan (bx – c):
Sketch two asymptotes.
bx – c = –π/2 and bx – c = π/2
Plot the zeros.
Midpoint between the asymptotes.
Plot additional points.
Midway between zero & VA = ± a.

8. Graph Transformation of Cotangent
To sketch the graph of y = a cot (bx – c):
Sketch two asymptotes.
bx – c = 0 and bx – c = π
Plot the zeros.
Midpoint between the asymptotes.
Plot additional points.
Midway between zero & VA = ± a.

9. Examples Sketch the graph of each function by hand. y = tan x/2
y = 2 cot x/3

10. .

11. Secant and Cosecant

12. Secant and Cosecant State the reciprocal function for each sec x =
csc x =
We will use the reciprocal functions to graph secant and cosecant.

13. Cosecant Where do the zeros of sin x occur?
If sin x is zero at these values, then what happens to csc x?
Where do the maximum values of sin x occur? What is the max value? What about minimum values?
What does this mean for csc x?

14. Graph Cosecant To graph csc x, Graph sin x. Sketch VA. Find max/min.
Create curve. .

15. Secant Where do the zeros of cos x occur?
If cos x is zero at these values, then what happens to sec x?
Where do the maximum values of cos x occur? What is the max value? What about minimum values?
What does this mean for sec x?

16. Graph Secant To graph sec x, Graph cos x. Sketch VA. Find max/min.
Create curve. .

17. Properties of sec x and csc x
Period
Domain
Range VA
Symmetry

18. Example 2
Sketch the graph of by hand. (Hint: graph sine first.) .

19. Example 3
Sketch the graph of by hand. (Hint: graph cosine first.) .

20. Homework 4.6
Worksheet 4.6