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Use your graphing calculator to explore sinusoidal functions.
Complete the following questions on page 516 (Investigate the Math, A - H) and page 517 (Reflecting, I - L) to investigate the relationship of the equation y = a sin b(x – c) + d to its graph.
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If you have any difficulty with these solutions, please contact your teacher before continuing.
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In Check It Out, you investigated the sinusoidal function y = a sin b(x – c) + d that represents the sine function. Consider a second type of sinusoidal function — the cosine function. From a graph, distinguishing the sine and cosine functions is difficult because they share similar characteristics. For this reason, you must be familiar with their equations.
In the following textbook examples, you will see how to determine the characteristics of a sine or cosine function from an equation and to verify your findings using the graphing calculator.
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Read pages 518-521 Examples 1 and 2
Complete the Your Turn questions on page 519 (a, b) and page 521 (a, b) for more practice in determining the characteristics of a sinusoidal function from its equation.
Click here to verify your answers.
Page 519
- amplitude:
equation of the midline:
range:
period:
horizontal translation:
Page 521
- amplitude:
equation of the midline:
range:
period:
horizontal translation:
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