The mean for average temperature in buffalo ,new york , is 47.5°. the temperture fluctuates 23.5° above and below the mean temperture . if t=1 present january ,the phase shift of the sine function is 4
a) write the funtion for the average monthly tempperature in buffalo
b) according to your modle ,what is the average tenperature in march ?
c) according to your modle ,what is the average tenperature in august ?

1) According to the statement, the Temperature will be modeled with a sine function.

2) a genaral sin function is of the type: Asin(mt + p) + M

where:

t is the variable

A is the amplitud: the fluction fluctuate +/- A units over the mean value. A = 23.5°

M is the mean value. M = 47.5°

m is the frequency, which we need to be 2π/12 (the complete cycle is 12 months) = m = π/6

p is the phase shift, which is 4. p = 4

Then:

a) the model or function is T(t) = 47.5° + 23.5* sin [ (π/6) t + 4]

b) T in march => t = 3

T(3) = 47.5° + 23.5° sin [ (π/6)*3 + 4] = 32.1 °

c) T in august => t = 8

T(8) = 47.5° + 23.5° sin [ (π/6)*8 + 4] = 69.7 °

Wow. that is a really cool question.