Graphs of the Sine and Cosine Functions

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Presentation transcript:

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

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

Copyright © 2013 Pearson Education, Inc. All rights reserved

Copyright © 2013 Pearson Education, Inc. All rights reserved

Copyright © 2013 Pearson Education, Inc. All rights reserved

Copyright © 2013 Pearson Education, Inc. All rights reserved

Copyright © 2013 Pearson Education, Inc. All rights reserved

Copyright © 2013 Pearson Education, Inc. All rights reserved

Copyright © 2013 Pearson Education, Inc. All rights reserved

Copyright © 2013 Pearson Education, Inc. All rights reserved

Copyright © 2013 Pearson Education, Inc. All rights reserved

Copyright © 2013 Pearson Education, Inc. All rights reserved

Copyright © 2013 Pearson Education, Inc. All rights reserved

Copyright © 2013 Pearson Education, Inc. All rights reserved

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

Copyright © 2013 Pearson Education, Inc. All rights reserved

Copyright © 2013 Pearson Education, Inc. All rights reserved

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

Copyright © 2013 Pearson Education, Inc. All rights reserved

Copyright © 2013 Pearson Education, Inc. All rights reserved

Copyright © 2013 Pearson Education, Inc. All rights reserved

Copyright © 2013 Pearson Education, Inc. All rights reserved

Copyright © 2013 Pearson Education, Inc. All rights reserved

Copyright © 2013 Pearson Education, Inc. All rights reserved

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

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

Homework 6.4: #15-19 odd, 21-30 all, 37, 41, 45, 59 Copyright © 2013 Pearson Education, Inc. All rights reserved