Transforming Graphs of Cosine Functions Mr

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Transforming Graphs of Cosine Functions Mr Transforming Graphs of Cosine Functions Mr. Peter Richard says: Don’t Cosine any Loans!

OBJECTIVES 1. Identify horizontal and vertical translations in the graph of sine function. 2. Graph the sine function with various phase shift and vertical shift. Copyright © by Houghton Mifflin Company, Inc. All rights reserved.

d: is the Vertical Shift Graphing y = a cosine b(x – c ) + d (x – c ): is the Horizontal Shift d: is the Vertical Shift Copyright © by Houghton Mifflin Company, Inc. All rights reserved.

Notes Over 6.4 Amplitude Period Translation left p Graphing a Horizontal Translation Graph the function. Amplitude Period Translation left p Copyright © by Houghton Mifflin Company, Inc. All rights reserved.

Phase Shift = to the right, since c > 0 Examples: Graph Amplitude =  3  = 3 Period = Phase Shift = to the right, since c > 0 - 3 3 Copyright © by Houghton Mifflin Company, Inc. All rights reserved.

Notes Over 6.4 Amplitude Translation down 2 Period Graphing a Vertical Translation Graph the function. Amplitude Translation down 2 Period Copyright © by Houghton Mifflin Company, Inc. All rights reserved.

Vertical Translation = 3 units upward, since d > 0 Examples: Graph Amplitude =  - 2  = 2 Period = Vertical Translation = 3 units upward, since d > 0 - 2 2 Copyright © by Houghton Mifflin Company, Inc. All rights reserved.

Translate the Cosines! Quiz: Page 760/761 # 16, 18, 20, 26, 34 Homework: # 15, 17, 21, 31, 39 Copyright © by Houghton Mifflin Company, Inc. All rights reserved.