Download presentation

Presentation is loading. Please wait.

Published byNia Mainer Modified over 3 years ago

1
**By: Taylor Pulchinski Daniel Overfelt Whitley Lubeck**

Sine & Cosine Graphs By: Taylor Pulchinski Daniel Overfelt Whitley Lubeck

2
**Equations y = a sin (bx-h)+ k y = a cos (bx-h)+k**

a = Amplitude (height of the wave) 2( )/b = Period (time it take to complete one trip around) h = Phase Shift (left or right movement) k = Vertical Shift (up or down movement)

3
**Examples y= 4 sin 3(x-2) Finding the Period and Amplitude Amplitude=4**

Amplitude y= a sin (bx-h)+k y= 4 sin (bx-h)+k Period y= a sin (bx-h) +k P= 2 / b P= 2 /3

4
**Examples of Non-Shifted Graphs**

y = sinx y = cos x

5
**Example Given the equation: Graph**

y = -2 sin (x-π/4) +1 amplitude = 2 period = 2π (2π/b = 2π/1 = 2π) phase shift = right π/4 vertical shift = up 1

6
**Example Given the Graph: write equation**

(graph goes by incriments of one) 1)Find what we know amplitude: = 4 Period = π/2 (2π/4 = 1π/2) phase shift = left π vertical shift = down 3 2) Plug into equation y = __cos__(x__)___ y = 4 cos 4 (x+π) -3

7
Example Story Problem A Ferris Wheel with a diameter of 60 feet completes one revolution every 5 minutes. The closest a chair gets to the ground is 2 feet. Write a cosine function for the height of the person above ground x minutes after boarding. 1) Find what we know Amplitude: 30 Vertical Shift: 32 Period: 2π/b = 5so 2π = 5bso 2π/5 = b phase shift: none 2) plug into equation y = ___ cos __(x___)____ y = 30cos(2π/5) x +32 graph start at 0 and goes to 62 on the y axis; graph starts at 0 and goes to 5 on x axis

8
**Story Problem Continued**

For the same problem, now write a sine function for the height of the person above ground x minutes after boarding 1) Find what we know amplitude: 30 Vertical Shift: 32 Period: 2π/b = 5 so 2π = 5b so 2π/5 = b Phase Shift: left (sine graph starts halfway between the starting point and middle...so 5/2 = 2.5/2 = 1.5) 2) Plug into equation y = __ sin____(x____)____ y = 30sin(2π/5)(x-1.25)+32 Graph tarts at 0 and goes to 62 on the y axis; graph starts at 1.25 and goes to 6 on the x axis

9
**Assessment . y= 2 sin 2x+ 4 A) 2 B) 2x C) 4 y= cos 3(x+1)-4 D) 6**

1&2 Find the amplitude of the function y= 2 sin 2x+ 4 A) 2 B) 2x C) 4 D) 6 y= -7 sin 3x-7 4 A) 3 B) -7 C) -7 D) 7 3. Find the Period of the function and use the language of transformations to describe the graph of the function related to y= cosx y= cos 3(x+1)-4 A) left 1 down 4 3 B) left 4 up 1 C) 3 up 1 left 4 D) 1 up 3 left 4

10
**Assessment Continued y= 2 sin 6 (x-3)+2 A) 2 down 3 up 2**

4. Find the Period of the function and use the language of transformations to describe how the graph of the function related to the graph y= cosx y= 2 sin 6 (x-3)+2 A) 2 down 3 up 2 B) right 2 down 3 6 C) right 3 up 2 3 D) 6 left 3 up 2

11
Assessment Continued 5. Sketch a Graph y= 6sin2x A) B) D) C)

12
Assessment Continued 6.Sketch a graph y= -2cos 2(x + )-2 8 A) B) C) D)

13
**Assessment Continued A) 4 sin 3x B) 3 sin 4x C) 3 sin 4(x+2)**

7&8 Write a Sin equation from the given graph. Then write a Cos equation A) 4 sin 3x B) 3 sin 4x C) 3 sin 4(x+2) D) 4 sin 3(x+2) A) 3 cos 4 (x+3) B) 3 cos 4 (x+2) C) 4 cos 4 (x+2) D) 4 cos 2 (x+3)

14
**Assessment Continued A) y=4 sin 3.5(x) +.5 B) y=3.5 sin 4(x) +3.5**

9. Write a Sin equation for the graph below. A) y=4 sin 3.5(x) +.5 B) y=3.5 sin 4(x) +3.5 C) y=3.5 sin 4(x) +.5 D) y=4 sin 4(x) +3.5

15
**Assessment Continued A)y=30sin 2 (x-.75)+32 3 B) y=32 sin 3 (x+3)+30 2**

10. Write a Sin equation when the diameter of a ferris wheel is 60 feet and it takes 3 minutes to make one round. The elevation is 2 feet off the ground. A)y=30sin 2 (x-.75)+32 3 B) y=32 sin 3 (x+3)+30 2 C) y=30 sin 2 (x+.75)+32 D)y= 30sin 2 (x-.75)-31

16
**Answer Key to Assessment**

2. C 3. A 4. C 5. A 6. B 7. B 8. B 9. C 10. A

17
**Supplement Activity Tic Tac Toe**

Directions: Two teams will play against one another. If you get a problem correct you can play an “x” or “o” depending on which team you’re on. First team to get three in a row wins. Problems: State the amplitude is, vertical and horizontal shifts, and what the period is. y=5sin(2x) y=2cos2(x+π/8)-2 y=cos(x/4) y=4sin4(x-2)+3 y=3sin2(x+4) y=sin(x-π/4)+1 y=2cos(x)+7 8. y=4sin2(x)-π/2

18
**Tic Tac Toe Answer Key 1.) Amplitude: 5 Period: π Vertical shift: none**

Phase shift: none 2.) Amplitude: 2 Vertical shift: down 2 Phase shift: left π/8 3.) Amplitude: 1 Period: 8π 4.) Amplitude: 4 Period: 1/2π Vertical shift: up 3 Phase shift: right 2 5.) Amplitude: 3 Period: π Vertical shift: none Phase shift: left 4 6.) Amplitude: 1 Period: 2π Vertical shift: up 1 Phase shift: right π/4 7.) Amplitude: 2 Vertical shift: up 7 Phase shift: none 8.) Amplitude: 4 Vertical shift: down π/2

19
**References http://graphsketch.com/**

The Great Ms. Scarseth

Similar presentations

Presentation is loading. Please wait....

OK

Aim: How do we sketch y = A(sin Bx) and

Aim: How do we sketch y = A(sin Bx) and

© 2018 SlidePlayer.com Inc.

All rights reserved.

Ads by Google

Ppt on famous indian entrepreneurs list Ppt on new project launch Ppt on internet banking free download Ppt on the art of war online Ppt on nitrogen cycle Ppt on purchase order Ppt on cross site scripting Ppt on global warming solutions Ppt on physical layer of osi model Pdf converter to ppt online