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

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.       

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)=       

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  

Lesson 1: The Graph of Cosecant     

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

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)=       

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

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

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)=       

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|:       

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|:     

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

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)=       

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

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

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.