TRANSLATIONS OF TRIGONOMETRIC GRAPHS 12 8 EXAMPLE 1

EXAMPLE 1: Find the period and the amplitude. Use it to find a possible

EXAMPLE 5 A State the amplitude, period, phase shift, vertical shift, and equation of

EXAMPLE 5 B State the amplitude, period, phase shift, vertical shift, and equation of

EXAMPLE 5 C State the amplitude, period, phase shift, vertical shift, and equation of

EXAMPLE 5 D State the amplitude, period, phase shift, vertical shift, and equation of

EXAMPLE 6 The height of water in a wave pool oscillates between a maximum

EXAMPLE 7 A Ferris wheel at the local fair has a diameter of 30

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TRANSLATIONS OF TRIGONOMETRIC GRAPHS 12. 8

EXAMPLE 1: Find the period and the amplitude. Use it to find a possible equation for the function.

PHASE SHIFTS

VERTICAL SHIFTS

MIDLINE

EXAMPLE 2 θ y θ y

EXAMPLE 3 θ y θ y

EXAMPLE 4 θ y θ y

EXAMPLE 5 A State the amplitude, period, phase shift, vertical shift, and equation of the midline, for the graph below. Then find a possible equation for the function.

EXAMPLE 5 B State the amplitude, period, phase shift, vertical shift, and equation of the midline, for the graph below. Then find a possible equation for the function.

EXAMPLE 5 C State the amplitude, period, phase shift, vertical shift, and equation of the midline, for the graph below. Then find a possible equation for the function.

EXAMPLE 5 D State the amplitude, period, phase shift, vertical shift, and equation of the midline, for the graph below. Then find a possible equation for the function.

EXAMPLE 6 The height of water in a wave pool oscillates between a maximum of 10 feet and a minimum of 6 feet. The wave generator pumps 3 waves per minute. Write a function that represents the height of the water at time t seconds. Assume that at t = 0, the height of the water is 8 feet.

EXAMPLE 7 A Ferris wheel at the local fair has a diameter of 30 ft. and a midline of 18 ft. This Ferris wheel makes one revolution every 60 seconds. If Amanda and Steve are riding on this Ferris wheel, write an equation that could be used to model the distance, d, that Amanda and Steve are from the ground as they ride the Ferris wheel, as a function of time, t. Assume that at t = 0, they are at the top of the Ferris wheel.