Answer:
T = - 7.5 Cos π/12( t - 4 ) + 10.5
Step-by-step explanation:
Given that the
Maximum temp. = 18 degree Celsius
Minimum temp. = 3 degree Celsius
The half way between 10 am and 10 pm is 4 am
The sine and cosine functions can be used to model fluctuations in temperature data through out the year. An equation that can be used to model these data is of the form:
T = A cos B(t - C) + D, where A,B,C,D, are constants, T is the temperature in °C and t is the hour (1–24)
A = amplitude = (Tmax - Tmin)/2
A = (3 - 18)/2 = - 15/2 = -7.5 ( note : after midnight)
B = 2π/24 = π/12
C = units translated to the right
C = 4
D = ymin + amplitude = units translated up
D = 7.5 + 3 = 10.5
The formula of the trigonometric function that models the temperature T in Johannesburg t hours after midnight we be
T = - 7.5 Cos π/12( t - 4 ) + 10.5
