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*Sketch sine and cosine graphs *Use amplitude and period *Sketch translations of sine and cosine graphs

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» One period = the intercepts, the maximum points, and the minimum points

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» Amplitude: of y = a sinx and y = a cosx represent half the distance between the maximum and minimum values of the function and is given by ˃Amplitude = I a I » Period: Let be be a positive real number. The period of y = a sinbx and y = a cosbx is given by ˃Period = (2π)/b

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» Sketch the graph y = 2sinx by hand on the interval [-π, 4π]

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» Sketch the graph of y = cos (x/2) by hand over the interval [-4π, 4π]

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» The constant c in the general equations ˃y = a sin(bx – c) and y = a cos(bx – c) create horizontal translations of the basic sine and cosine curves. » One cycle of the period starts at bx – c = 0 and ends at bx – c = 2π » The number c/b is called a phase shift

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» Sketch the graph y = ½ sin (x – π/3)

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» Sketch the graph y = 2 + 3 cos2x

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» Find the amplitude, period, and phase shift for the sine function whose graph is shown. Then write the equation of the graph.

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» For a person at rest, the velocity v (in liters per second) of air flow during a respiratory cycle (the time from the beginning of one breath to the beginning of the next) is given by where t is the time (in seconds). (inhalation occurs when v> 0 and exhalation occurs when v < 0 ) a)Graph on the calculator b)Find the time for one full respiratory cycle c)Find the number of cycles per minute d) The model is for a person at rest. How might the model change for a person who is exercising?

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» A company that produces snowboards, which are seasonal products, forecast monthly sales for 1 year to be where S is the sales in thousands of units and t is the time in months, with t = 1 corresponding to January. a)Graph the function for a 1 year period b)What months have maximum sales and which months have minimum sales.

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» Throughout the day, the depth of the water at the end of a dock in Bangor, Washington varies with the tides. The table shows the depths (in feet) at various times during the morning. » Use a trigonometric function to model this data. » A boat needs at least 10 feet of water to moor at the dock. During what times in the evening can it safely dock? Time12am2 am4 am6 am8 am10am12pm Depth, y3.17.811.310.96.61.7.9

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Amplitude, Period, and Phase Shift

Amplitude, Period, and Phase Shift

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