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Sinusoidal Graphs

Part 5: Summary

The following questions refer to a sinusoidal function of the form

y(t) = A + B sin [ C (t - t0) ]

or

y(t) = A + B cos [ C (t - t0) ].

  1. How is A related to the average value of y(t)?

  2. How are A and B related to the largest and smallest values of y(t)?

  3. How is C related to the period of the function?

  4. What effect does t0 have on the graph of the function?

  5. If you know the largest and smallest values of y, as well as the period, how can you determine all four coefficients?

  6. What would you expect to be the period of an hours-of-sunlight function? Why?

  7. How are the basic sine and cosine graphs related to each other?

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