Explanation:
a)
the minimum is -79°.
the maximum is -5°.
b)
the period of local maximum to local maximum is 700 days from -5° to -8°.
the period of local minimum to local minimum is also 700 days from -79° to -78°.
that suggests the sine function here has a wavelength of period of 700 days. so, 0 .. 2pi rad corresponds to 0 .. 700 days.
the maximum temperature (-5°) corresponds to pi/2 (= 2pi/4 corresponding to 700/4 = 175 days), the minimum (-79°) to 3pi/2 (= 3 × pi/2 = 3×175 = 525 days).
0 and pi must then correspond to the middle of the extremes: (-5 + -79)/2 = -84/2 = -42°.
the amplitude (from the middle to the maximum or minimum) is then |-42 - -5| = 37°.
so, our approximate model would be
T(n) = -42 + 37×sin(n×2pi/700)
it has to start at about -42° with n=0, then it would reach from there a maximum (as the temperature first goes up by about 37°) at about day 175, goes down to about -42° again at day 350, goes down to the minimum at about day 525. and then back up to about -42° at day 700.
with every change from middle to maximum, maximum to middle, middle to minimum, minimum to middle being about 37°.
c)
the year on Mars would be a long as the period of our sine curve : 700 days (e.g. from the warmest day to the next warmest day).