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 °