T5.1d To Graph Vertical Translation 4-20-17 T5.1d To Graph Vertical Translation

As a group, find the equation of this graph As a group, find the equation of this graph. I will call on someone, please make sure you have it: y = 4 sin (x) 2

Active Learning Assignment? Amplitude……….._______ Vertical Translation_______ Period Frequency…_______ Period Length……._______ Phase shift……….._______

* * LESSON: Standard form for Sine Function: y = a*sin b * (x – h) + k Standard form for Cosine Function: y = a*cos b * (x – h) + k Today we will be looking at how “k” affects the sin and cos curves. Let’s look at Desmos. * * y = a*sin b * (x – h) + k REALLY comes from: y – k = a*sin b * (x – h)

Graph y = 2 sin (x) + 3 OR could be: y = 3 + 2 sin (x) NOT 5! 2 y =3 1 Amplitude……….._______ Vertical Translation_______ Period Frequency…_______ Period Length……._______ Phase shift……….._______ 2 5 y =3 3 1 1 Beginning ¼ ½ ¾ End 2π 1 Period π “0” Max “0” Min “0”

This is the y axis: → (x = 0) Graph y = 2 sin (x) + 3 Please pay attention: 5 This is the x axis: (y = 0) → 3 1 This is the y axis: → (x = 0) Do not “highjack” the coordinate axes and put your labels on them!!! For example, in this problem, DO NOT CHANGE THE X AXIS TO “3”. You must show your own translation or shift!!!

Graph y = – 2 + 5 cos (x) OR could be: y = 5 cos (x) – 2 NOT 3! 5 Amplitude……….._______ Vertical Translation_______ Period Frequency…_______ Period Length……._______ Phase shift……….._______ 5 y = -2 3 1 -2 -7 Beginning ¼ ½ ¾ End 2π 1 Period π Max “0” Min “0” Max

As a group, find the equation of this graph As a group, find the equation of this graph. I will call on someone, please make sure you have it: 6 y = 2 cos (x) 4 + 3 4

Graph y = ½ sin ¼ (x) + 3 ½ y = 3 ¼ 1 Period “0” Max “0” Min “0” 3 Amplitude……….._______ Vertical Translation_______ Period Frequency…_______ Period Length……._______ Phase shift……….._______ 3 ½ y = 3 ¼ Beginning ¼ ½ ¾ End 1 Period “0” Max “0” Min “0”

Active Learning Assignment: Graph I Handout: 23-29 odds