The equation of the temperature T as a function of time t is of the form:
where a is the amplitude, `(2pi)/b` is the period, c is the horizontal shift or phase and d is the vertical shift.
The difference between the time at the high and the time at the low is equal to half the period, then:
And the period is `26x2=52min`
To calculate the horizontal shift, determine the t intercept before the high.
The vertical shift is equal to the average of the high and low.
Therefore the equation would be:
To compute the temperature, substitute 0 for t in (1)
Thus the temperature when they started timing was 104.8 degrees.
The function can also be expressed as a cosine with a phase shift to the left. The minimum before the maximum at t=32 is at t=32=26=6, therefore the next maximum is at t=20 and the cosine function is: