For this problem, you will be modeling the horizontal and vertical displacement of a Ferris wheel using the following equations:

x $=$ Asin$($Bt$)+$ Cx

y $=-$Acos$($Bt$)+$ Cy

In this equation, x and y are the horizontal and vertical displacements, A is the amplitude, B relates to the period, C is the vertical shift, and t is the time.

a$)$ Create an array t from $0$ to $60$ minutes in increments of $15$ seconds.

b$)$ The amplitude for both x and y is $25$ meters. Assign this value to A$.$

c$)$ Each revolution of the Ferris takes exactly $15$ minutes. Determine the period for both x and

y$.$ Assign the value to B$.$

d$)$ The vertical shift for x and y is $0$ and $30$ meters respectively. Assign these values to C$.$

e$)$ On a $3$x$1$ subplot grid, plot the following after calculating x and y:

i$)$ Plot the horizontal displacement vs$.$ time with a magenta dashed line. Title this: $$Ferris Wheel Horizontal Displacement$.$

ii$)$ Plot the vertical displacement vs$.$ time with a red dash$-$dotted line. Title this: $$Ferris Wheel Vertical Displacement$.$

iii$)$ Plot the vertical displacement vs$.$ horizontal displacement with green square markers. Title this: $$Ferris Wheel Model$.$

f$)$ Make sure to appropriately label the x$-$axis and y$-$axis for each plot $($include the units as well$).$