Math(trigonometry

Question

You are standing at a base of a Ferris Wheel which is 4 m above ground while your friend is riding. The Ferris Wheel is 8m in diameter. Describe how the shape of the sine curve models the distance your friend is to the platform you are on by determining the following details. Identify the function that will model this situation. Ie. Determine the equation

Property	Put your equation in this box:
maximum
minimum
amplitude
Axis of the curve
period
domain
range
y-intercept
x-intercepts (zeros)
intervals of increase
intervals of decrease

Answer 1

the sinusoidal function modeling the position on the ferris wheel is

f(t) = Asin(B(t+C) + D where A =amplitude, C= phase shift, if any, D = midline, 2pi/B=period

8 meters in diameter means the amplitude=A=8/2 = 4

3 meters off the ground makes the midline 3+4 = 7

without more information, maybe make B=1 and C=0

f(t) = 4sint + 3

maximum height = 8+3 = 11

minimum point = 3

period = 2pi

domain is [3,11]

range [0 infinity) although realistically the upper bound is not infinity but closer to the time period the ferris wheel runs for the price of one ticket

y intercept is (0,0)

x intercepts are 2npi where n = any integer

intervals of increase are when the ferris wheel is moving from min to max (0,pi/2), (3pi/2, 5pi/2), (7pi/2,9pi/2), ...

intervals of decrease are when the wheel is moving from max to min which are all the intervening open intervals that are not above: (pi/2,3pi/2), (5pi/2,7pi/2), (9pi/2, 11pi/2), ....