lets assume the sine function is in the following form,

`y = Asin(bt+c)+D`

now according to the data, the minimum height is 900 m and maximum height is 1500 m. These two values corresponds to the minimum and maximum values that sine can get, which are -1 and +1 respectively.

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lets assume the sine function is in the following form,

`y = Asin(bt+c)+D`

now according to the data, the minimum height is 900 m and maximum height is 1500 m. These two values corresponds to the minimum and maximum values that sine can get, which are -1 and +1 respectively.

so,

900 = A(-1)+D

`900 = -A+D ` ------1

and

1500 = A(1)+D

`1500 = A+D` ------2

solving 1 and 2 you will get,

A = 300 and D = 1200.

So the equations reduces to,

`y = 300sin(bt+c)+1200`

but we know at t = 0, y = 900 (At the lowest point)

Then,

`900 = 300 sin(c)+1200`

This gives,

`sin(c) = -1`

`c = sin^(-1)(-1)`

`c = -pi/2`

The other thing we know is, it has period of 75 minutes,

then, it reaches its first maximum at 75/2 minutes which is 1500 m

`1500 = 300sin(b*(75/2) -pi/2)+900`

`300sin(b*(75/2) -pi/2) = 300`

`sin(b*(75/2) -pi/2) = 1`

`b*(75/2) -pi/2 = pi/2`

`b*(75/2) = pi`

`b = (2pi)/75`

Therefore teh required equation is,

`y = 300sin((2pit)/75-pi/2)+1200`