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!!
Top Related