SOLUTION: The top of a flagpole is swaying in the wind. The top sways from 6 cm to the right of its resting position (+6 cm) to 6 cm to the left of its resting position (-6 cm) and back to t

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Question 1140805: The top of a flagpole is swaying in the wind. The top sways from 6 cm to the right of its resting position (+6 cm) to 6 cm to the left of its resting position (-6 cm) and back to the right 6 times per second. Determine the equation of a sinusoidal function that describes the distance the top of the pole is from its resting position in terms of time.
Answer by Theo(13342) (Show Source):
You can put this solution on YOUR website!
the general equation of the sine function is:

y = a * sine (b * (x - c)) + d

a is the distance from the center line of the sine wave function.
b is the frequency
c is the horizontal displacement
d is the vertical displacement.

if a = 1, then the distance from the center line is plus or minus 1.

when a = 6, the distance from the center line will be plus or minus 6.

if b = 1, then the frequency is one full cycle every 360 degrees.

there is a relationship between frequency and period.

the frequency is the number of full cycles within 360 degrees.
the period is the number of degrees each full cycle will take.

the formula for period is period = 360 / frequency.
the formula for frequency is frequency = 360 / period.

if you want to get 6 full cycles every second, then the period needs to be 1/6 of a second.

when the period is 1/6 of a second, the frequency needs to be 360 / (1/6) = 360 * 6 = 2160.

with an amplitude of plus or minus 6 and a frequency of 2160, the sine wave formula becomes:

y = 6 * sine (2160 * x)

there is no horizontal displacement, so c is equal to 0 and drops out of the equation.

there is no vertical displacement, so d is equal to 0 and drops out of the equation.

the graph looks like this.

i marked up the number of cycles in 1 second.
i also marked up the peaks of each cycle.

that looks like this.