2.6 Graphing Sine and Cosine Functions

Warm-up (IN)1. Identify the transformations from to

Learning Objective: To graph sine and cosine functions and to determine the amplitude and period of sinusoidal functions.

2y xvertical stretch by 3

vertical shift down 2

vertical stretch by 2, horizontal shift right 3

1 vertical compression by , horizontal compression by 2, 5

horizontal shift left 1, vertical shift down 4

2a. 3y x2b. 7y x 2c. 2 3y x

21d. 2 1 45

y x

NOTES"Sinusoidal FUNctions" y f x sin x

x=angle in radians

F(x)=value of function

cosf x x

tanf x x

cscf x x

secf x x cotf x x

Sin and Cos functions have a period of2So we will graph the interval 0 2x

x sin x0 02

1

1

2 3

2 2

1

032 1

2 0

Cycle - 1 period, or…the time it takes to repeat

sinf x x

Transformations!

sinf x x h kA

A amplitude horiz. stretch/

compression

h horiz. shift

k vert. shift

Ex 1 - Use sin to graph sin4

y x y x

Shifts right units

4

Ex 2 - Use sin to graph sin 2y x y x Shifts up 2 flips

x cos x0 12 0

1

2 3

2 2

1

132 0

2 1

cosf x x

Ex 3 - Use cos to graph 2cosy x y x Amp is 2

Ex 4 - Use cos to graph cos 3y x y x Horiz compression by 3

3 2x 23

x

Find the period!

Divide by 4 to get units

234

6

HW – pg. 186 #9-18,21-23,26-30,35

Out – Describe the transformations of the sine curve.Summary – I have a question about… or… Wow! I…

Don’t forget about POW!!