Find the values of Y Z k and f to best fit the curve between

Find the values of Y, Z, k, and f, to best fit the curve between the function X(t) and the values of the temperature listed below.

X(t) = Y+(Z*sin((k*t)+f))

Temperature values:

Solution

minimum = 38

maximum =48

All other values lie between these two

Hence middle line = 43 (average of 38 and 48)

X(t) = 48+ or - z sin (kt+f)

As variation max is 5 on both the sides

z =5

Hence x(t) = 48+5sin(kt+f)

f and k will not be unique