Please grab the warm up off of the chair in the front of the room and begin working!

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Merryl Hawkins
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1 Please grab the warm up off of the chair in the front of the room and begin working! add the x! #2 Fix to y = 5cos (2πx 2) + 9 Have your homework out on your desk to be checked. (Pre requisite for graphing Sine and Cosine) Feb 5 8:39 PM 1

2 Feb 8 10:11 PM 2

3 Check your homework from last night Feb 8 10:04 PM 3

4 This quiz is coming... Feb 2 6:56 AM 4

5 Objective: Students will be able to identify the transformations from a trigonometric function and sketch the graph. Feb 5 8:42 PM 5

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13 Trigonometric parent functions: y = sin x How long does sine take to complete one cycle? Period: How long the trig. function takes to complete one cycle. Feb 5 8:44 PM 13

14 Trigonometric parent functions: what is cosine's period? y = cos x Feb 5 8:54 PM 14

15 How can you remember these graphs? y = sin x "up hump down hump" y = cos x "ovaries" π 2 π 3π 2 2 π 1 π 2 π 3π 2 2 π Feb 5 9:24 PM 15

16 Recall transformations of other parent functions: y = a sin b(x c) + d inside opposite outside same a vertical stretch/shrink b horizontal stretch/shrink c shift left and right d shift up and down Trig meaning: amplitude period length phase shift location of mid line Feb 5 8:43 PM 16

17 Steps for identifying the transformations. y = a sin b(x c) + d 1). Factor what's on the inside first so there is NO coefficient on x. 2). look at d => determines the location of the mid line. 3). look at a => determines the distance the function travels away from the mid line. 4). look at c => determines the shift right or left 5). look at b => determines the period of the function Period = 2 π b Feb 4 12:55 PM 17

18 Recall the graph of sine. y = sin x 1 1 π 2 π 3π 2 2 π Period: Amplitude: Phase shift: Mid line: You now do the same for the cosine graph Feb 5 9:21 PM 18

19 For example: y = 4 sin x + 5 What transformations do you see here? 1). Draw the mid line (sin up hump down hump) (cos ovaries) 2). Mark the amplitude (distance away from mid line 3). Sketch graph appropriately based on trig function Feb 5 9:19 PM 19

20 For example: y = 6 cos x 3 Feb 5 9:18 PM 20

21 Let's add a "c" y = 2 sin (x π) + 4 1). Draw mid line. 2). Mark the amplitude. 3). Shift starting point right or le Feb 4 1:09 PM 21

22 Let's add a "c" continued... y = 5 cos (x + ) 8 3π 4 Feb 4 1:12 PM 22

23 Let's put it all together: Practice Step 1: On your communicator y = a sin b(x c) + d 1). Factor what's on the inside first so there is NO coefficient on x. y = 4 sin (3x 2π) + 8 y = 5 sin (2x π 3 ) π y= 6 cos ( x ) Feb 4 1:02 PM 23

24 Let's put it all together: y = 4 sin (3πx 2π) + 8 Feb 4 1:14 PM 24

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26 π y = 5 sin (2x 3 ) + 4 Feb 4 1:17 PM 26

27 1 3π y= 6 cos ( x ) Feb 4 1:27 PM 27

28 Exit Slip: On a piece of paper please answer the following questions. 1. What is the period of y = sin(x)? 2. What transformation moves the graph left or right? 3. What transformation moves the graph up or down? 4. What transformation makes the graph move more distance away from the midline? 5. What transformation changes how long it takes a sinusoidal function to complete one full rotation? Feb 3 6:32 AM 28

29 Feb 5 2:39 PM 29

Section 8.4: The Equations of Sinusoidal Functions

Section 8.4: The Equations of Sinusoidal Functions In this section, we will examine transformations of the sine and cosine function and learn how to read various properties from the equation. Transformed