Algebra II - Staublin

The general equations for the sin and cosine functions are:

y = asin(bx+c)+d    and    y = acos(bx+c)+d

Go to the link at the bottom of the page and use the drop-down menus to explore the effect that a, b, c, and d have on the sin and cos functions. Draw some pictures and keep some notes so that you have a record of your conclusions.

Use a web-browser to look up the following terms:

• amplitude
• period
• phase shift
• vertical translation

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Change the values of a, b, c and d one at a time.

• What effect does changing the value of a have on the graph?
• What effect does changing the value of b have on the graph?
• What effect does changing the value of c have on the graph?
• What effect does changing the value of d have on the graph?

Given what you have discovered, predict what the graph of y = 8 cos(2x – 30°) + 7 would look like. What are its amplitude and period?

Go to Illuminations - Graphing General Trigonmetric Functions