1. Essential Question: How do we graph trig functions, their transformations, and inverses? Graphs of Sine and Cosine

2. Graph y = sin  sin  0° 0.707 45° 90° 1 135° 0.707 180° 225°
90º
-90º
270º
-270º
180º
360º -1 -2 2 1 0°
0.707
45°
90° 1
135°
0.707
180°
225°
-0.707 -1
270°
-0.707
315°
360°

3. y = sin x 2 1 -90º 90º -270º 270º -1 -2 Maximum Maximum intercept
Minimum
Minimum -2

4. y = sin x
Period: the least amount of space (degrees or radians) the function takes to complete one cycle. 2 1
-90º
90º
-270º
270º -1 -2
Period: 360°

5. In other words, how high does it go from its axis?
y = sin x
Amplitude: half the distance between the maximum and minimum 2
Amplitude = 1 1
-90º
90º
-270º
270º -1 -2
In other words, how high does it go from its axis?

6. Graph y = cos cos   1 0.707 -0.707 -1 -0.707 0.707 1 2 1 -1 -2 2 1
0.707
-0.707  -1
-0.707
0.707 2 1

7. y = cos x -2 -  2 2 1 -1 -2 Maximum Maximum intercept intercept
Minimum
Minimum -2

8. y = cos x -2 -  2 Period: 2
Period: the least amount of space (degrees or radians) the function takes to complete one cycle. 2 1
-2 -  2 -1 -2
Period: 2

9. How high does it go from its axis?
y = cos x
How high does it go from its axis? 2
Amplitude = 1 1
-2 -  2 -1 -2

10. y = sin x
y = cos x 2 1 -1 -2

11. y= sin and y = cos are the Parent functions.
Changing the equations changes the appearance of the graphs
We are going to talk about the AMPLITUDE, TRANSLATIONS, and PERIOD of relative equations

12. y = -2 + 3 cos (3θ) (degrees) Ex Graph 3 x y high 1 0° amplitude = -2
mid
30°
period =
= 120°
low
60° -5
90°
vertical translation:
down 2 -2
mid
120° 1
high
1) divide period by 4 to find increments
= 30
table goes in increments of 30
2) graph

13. y = 1 + 3 sin (2 ) =  Ex #6c Graph 3 up 1 x y mid 1 amplitude = high4
period = 1
mid
vertical translation:
up 1 -2
low
mid
1) divide period by 4 to find increments 1
On Calculator, go to table setup and change independent to ask.
table goes in increments of
2) graph

14. PRACTICE 4.6 – HW - Worksheet