A merry-go-round takes 15 seconds to complete one revolution/spin. Within that time, each horse moves up and down five times. The vertical motion of the horse spans a range of 50 cm, and the horse is 1 m high at its vertically centre position. (Hint: Sine Wave/Function)
a. Sketch a graph of the height of the horse over time for one complete revolution/spin of the ride, starting with the horse at its lowest position, where h is the height of the horse in centimetres and t is the time elapsed in seconds.
b. State the equation of the SINE function that relates the height of the horse, h, as a function of time, t.
We begin by deriving the sine function (part b). Assume that everything is in degrees.
Since the cycle is 15 seconds, and the hourse moves up and down five times, that means the horse moves up and down (one vertical cycle) every 3 seconds. This is the period.
Sinus cosinus functions