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

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°

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

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°

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?

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

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

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

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

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

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

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 120 4 = 30 table goes in increments of 30 2) graph

y = 1 + 3 sin (2 ) =  Ex #6c Graph 3 up 1 x y mid 1 amplitude = high 4 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

PRACTICE 4.6 – HW - Worksheet