Suppose Ken is riding a Ferris wheel. The maximum height he attains is 16 m and the minimum height is 0 m. The time it takes to make one cycle is about 6 minutes. Draw a graph which represents this scenario if Ken starts at a height of about 8 m.

Please can you explain how you know to use what points.

Julius
May 19, 2017

#1
**+2 **

Here's the graph you need : https://www.desmos.com/calculator/e3rve2bfvr

Using y = Asin (Bx + C) + D

We can divide the normal period of the sine (2 pi) into 6 equal parts....so that each part (one minute) is [2pi / 6] rads = pi/ 3 rads = B.......

After 1.5 minutes the normal sine will reach its max height = 1

Note..... sin [ pi (1.5)/3] =

sin (pi/2) = 1

And it will return to the midline point of y= 0 after 3 minutes since sin (pi (3)/ 3) = sin (pi) = 0

And it will reach a minimum of y = -1 after 4.5 minutes because sin (pi (4.5)/3) = sin (3pi/2) = -1

And it returns to the midline (the starting height) of y = 0 at 6 minutes since sin (pi * 6/ 3) =

sin (2pi) = 0

There is no shift left or right, so "C" = 0

Next we need to make some adjustments

We know that the amplitude is 8 because the graph rises 8 units up and down from the midline of y = 0 ....so "A' = 8

But......the midline of the graph starts at 8 so we need to append 8 to the function.....so, "D'" = 8 will give us that shift

I hope that helps ....!!!!

CPhill
May 19, 2017