Modeling with Periodic Functions Answers

b = pi/2pi2pi

a =

k =

The period is seconds.

b = pi/20pi/10pi/5

a =

The period is seconds.

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Graph the function using the graphing calculator. Find the least positive value of t at which the pendulum is in the center.t = sec

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a is the length of the bladeheight of the windmillnumber of rotations per minute.

The depth of the water at the end of a pier changes periodically along with the movement of tides. On a particular day, low tides occur at 12:00 am and 12:30 pm, with a depth of 2.5 m, while high tides occur at 6:15 am and 6:45 pm, with a depth of 5.5 m. Let t = 0 be 12:00 am.Graph the equation d = -1.5 cosine left-bracket StartFraction 4 pi over 25 EndFraction t right-bracket + 4 that models the situation using a graphing calculator and use it to answer the following questions.

The graph of these points follows a path resembling a .

A graph has month on the x-axis and temperature in degrees Fahrenheit on the y-axis. Month 0 is 23; Month 1 is 35; month 2 is 48; month 3 is 65; month 4 is 74; month 5 is 80; month 6 is 76; month 7 is 64; month 8 is 50; month 9 is 32; month 10 is 24; month 11 is 20. Use the graph to write an equation y = acos[b(x – h)] + k to model the situation.The amplitude is ,

The blades of the windmill turn on an axis that is 5152025 feet from the ground.

To the nearest thousandth, find the position of the pendulum when t = 4.25 sec. d = in.