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Graphs of the Sine and Cosine Functions

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1 Graphs of the Sine and Cosine Functions
Section 6.4 Graphs of the Sine and Cosine Functions Copyright © 2013 Pearson Education, Inc. All rights reserved

2 Graph functions of the form y=Asin(ωx) using transformations.
Objectives Graph functions of the form y=Asin(ωx) using transformations. Graph functions of the form y=Acos(ωx) using transformations. Determine the amplitude and period of sinusoidal functions. Graph sinusoidal functions using key points. Find an equation for a sinusoidal graph. Copyright © 2013 Pearson Education, Inc. All rights reserved

3 Copyright © 2013 Pearson Education, Inc. All rights reserved

4 Copyright © 2013 Pearson Education, Inc. All rights reserved

5 Copyright © 2013 Pearson Education, Inc. All rights reserved

6 Copyright © 2013 Pearson Education, Inc. All rights reserved

7 Copyright © 2013 Pearson Education, Inc. All rights reserved

8 Copyright © 2013 Pearson Education, Inc. All rights reserved

9 Copyright © 2013 Pearson Education, Inc. All rights reserved

10 Copyright © 2013 Pearson Education, Inc. All rights reserved

11 Copyright © 2013 Pearson Education, Inc. All rights reserved

12 Copyright © 2013 Pearson Education, Inc. All rights reserved

13 Copyright © 2013 Pearson Education, Inc. All rights reserved

14 Copyright © 2013 Pearson Education, Inc. All rights reserved

15 Amplitude Copyright © 2013 Pearson Education, Inc. All rights reserved

16 Copyright © 2013 Pearson Education, Inc. All rights reserved

17 Copyright © 2013 Pearson Education, Inc. All rights reserved

18 Determine the amplitude and period of y = – 4 cos (3x)
Copyright © 2013 Pearson Education, Inc. All rights reserved

19 Copyright © 2013 Pearson Education, Inc. All rights reserved

20 Copyright © 2013 Pearson Education, Inc. All rights reserved

21 Copyright © 2013 Pearson Education, Inc. All rights reserved

22 Copyright © 2013 Pearson Education, Inc. All rights reserved

23 Copyright © 2013 Pearson Education, Inc. All rights reserved

24 Copyright © 2013 Pearson Education, Inc. All rights reserved

25 A = 3 Copyright © 2013 Pearson Education, Inc. All rights reserved

26 Note that this is a reflection over the x-axis of the sine function so while the amplitude is 2, A = –2. A = –2 Copyright © 2013 Pearson Education, Inc. All rights reserved

27 Homework 6.4: #15-19 odd, all, 37, 41, 45, 59 Copyright © 2013 Pearson Education, Inc. All rights reserved


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