trig wheel 6
A Ferris wheel reaches a maximum height of 24 m. The lowest point of the wheel is 4 m above ground. The wheel travels one complete revolution in 1 minute (60 seconds). Model the wheel using a sine wave function. The passenger boards the Ferris wheel at its lowest point. As before the function has amplitude (A), frequency (B), horizontal shift (C) and vertical shift (D). You should practise drawing this wave form before attempting any of these questions. This includes understanding how to express the cosine waveform as a sine wave.
Draw a diagram to help you with the problem.
Draw a diagram to help you with the problem.
amplitude A
A = (max - min)/2 = (24 - 4)/2 = 10m
frequency B
The frequency B is equal to the distance of 2π divided by the time for one period, which is:
horizontal shift C
The cosine wave is the same as a sine wave that has been translated to the right on the x axis. It has moved by 1/4 or π/2. In this example that distance along the x axis happens to be 15 seconds (same as in Trig Wheel 5). So the value of C = 15. It is written as (t - 15)
vertical shift D
(max + min)/2 = (24 + 4)/2 = 14 m. So D = 14 and the equation for the function becomes.