TRIG WHEEL 7
A Ferris wheel reaches a maximum height of 18 m. The lowest point of the wheel is 2 m above ground. The wheel travels two complete revolutions 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 = (18-2)/2 = 8 m.
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 7.5 seconds. So the value of C = 7.5. It is written as (t - 7.5)
Vertical shift D
(max + min)/2 = (18 + 2)/2 = 10 m. So D = 10 and the equation for the function becomes.
on the calculator
Remember that not all the equation is showing on the calculator screen, the "+10" is off screen!