T = - 7.5 Cos π/12( t - 4 ) + 10.5 varies over the day in a periodic way that can be modeled approximately by a trigonometric function.
<h3>What is
trigonometric function?</h3>
The trigonometric functions are actual functions that relate a right-angled triangle's angle to side length ratios. They are extensively employed in all geosciences, including navigation, solid mechanics, celestial mechanics, geodesy, and many more.
<h3>According to the given information :</h3>
Maximum temp. = 18 degree Celsius
Minimum temp. = 3 degree Celsius
The half way between 10 am and 10 pm is 4 am
Temperature data changes throughout the year can be modeled using the sine and cosine functions. The following form of equation can be used to model these data:
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
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
To know more about trigonometric function visit:
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