A bike is on a stand such that the highest point of the back wheel is 47 inches above the ground. If the pedal is turned counter clockwise, the back wheel turns CCW also. The tire valve on the back wheel is 12 inches from the wheel's center of rotation.
You will define three functions below whose input is angle measure a, the number of radians swept by the pedal CCW from its 3 o'clock position, and whose output relates to the position of the tire valve
a) Define a function that gives the horizontal distance of the tire valve to the right of the tire's vertical diameter ...
i) ... in radius lengths, if both the pedal and tire valve start in their respective 3 o'clock positions together, and the tire rotates 1/3 as much as the pedal rotates.
f(a)=
ii) ... in radius lengths, if the tire valve starts π/4 radians CCW from 3 o'clock, and one revolution of the pedal results in one revolution of the tire.
g(a)=
iii) ... in inches, if both the pedal and tire valve start in their respective 3 o'clock positions together, and 1/2 of a revolution of the pedal results in one revolution of the tire.
h(a)=