1. 4.6(c) Notes: Reciprocal Functions & Damped Trig Graphs
Date:
4.6(c) Notes: Reciprocal Functions & Damped Trig Graphs
Lesson Objective: To understand the graph of y = csc x, y = sec x and damped trig graphs.
CCSS: F-TF Extend the domain of tri­go­no­me­tric functions using the unit circle.
You will need: Colored pens

2. Lesson 1: The Graph of Cosecant
Use highlighter or pencil to divide the coordinate plane in half as shown. Add the other vertical axis as shown.   

3. Lesson 1: The Graph of Cosecant
Graph y = sin x in dotted red ink on the left side.
|A|: 2. Period, 2π/B:
Interval, Period/4: 4. Phase Shift, C/B:
Vertical Shift, D:
Max: , Min:
5 Key Points:
(x1, y1)= (x2, y2)= (x3, y3)= (x4, y4)= (x5, y5)=   

4. Lesson 1: The Graph of Cosecant
Complete the table. Graph y = csc x in solid red ink.    x π 12 6 4 3 2 2π 3π 5π
11π
sin x
csc x

5. Lesson 1: The Graph of Cosecant   

6. Lesson 2: The Graph of Cosecant Shortcut!
Graphing y = A csc Bx and y = A sec Bx:
x-int of y=A sin Bx or y=A cos Bx
Minimum of csc or max of sin or cos
Maximum of csc or min of sin or cos   

7. Lesson 2: The Graph of Secant
Graph y = cos x in dotted blue ink on the right.
|A|: 2. Period, 2π/B:
Interval, Period/4: 4. Phase Shift, C/B:
Vertical Shift, D:
Max: , Min:
5 Key Points:
(x1, y1)= (x2, y2)= (x3, y3)= (x4, y4)= (x5, y5)=   

8. Lesson 2: The Graph of Secant Graph y = sec x. 1. Asymptotes:
2. Minimum, y = D + |A|:
3. Maximum, y = D – |A|:   

9. Lesson 3: Graphing y = A csc Bx Graph y = csc(x + π/4).  

10. Lesson 3: Graphing y = A csc Bx
Graph y = sin(x + π/4) in dotted green ink.
|A|: 2. Period, 2π/B:
Interval, Period/4: 4. Phase Shift, C/B:
Vertical Shift, D:
Max: , Min:
5 Key Points:
(x1, y1)= (x2, y2)= (x3, y3)= (x4, y4)= (x5, y5)=   

11. Lesson 3: Graphing y = A csc Bx Graph y = csc(x + π/4). 1. Asymptotes:
2. Minimum, y = D + |A|:
3. Maximum, y = D – |A|:   

12. Lesson 3: Graphing y = A csc Bx
Graph y = csc(x + π/4).
1. Asymptotes:
2. Minimum, y = D + |A|:
3. Maximum, y = D – |A|:   

13. Lesson 4: Graphing y = A sec Bx Graph y = 2 sec 2x.  

14. Lesson 4: Graphing y = A sec Bx
Graph y = 2 cos 2x in dotted purple ink.
|A|: 2. Period, 2π/B:
Interval, Period/4: 4. Phase Shift, C/B:
Vertical Shift, D:
Max: , Min:
5 Key Points:
(x1, y1)= (x2, y2)= (x3, y3)= (x4, y4)= (x5, y5)=   

15. Lesson 4: Graphing y = A sec Bx Graph y = 2 sec 2x. 1. Asymptotes:
2. Minimum, y = D + |A|:
3. Maximum, y = D – |A|:   

16. Lesson 4: Graphing y = A sec Bx
Graph y = 2 sec 2x.
1. Asymptotes:
2. Minimum, y = D + |A|:
3. Maximum, y = D – |A|:   

17. 4.6(c): Do I Get It? Yes or No
1. Use the graph of y = 2 sin 2x to obtain the graph of y = 2 csc 2x.
2. Use the graph of y = -3 cos x/2 to obtain the graph of y = -3 sec x/2.