Trig help needed please?

Question

The mean daily temperature in degrees Fahrenheit of a certain city on the xth day of the year is approximated by the function f(x) = 64 + 27cos[(2pi/365)(x+145)]

a) Find the amplitude of the function

b) Find the period of the function

c) Find the highest and lowest mean daily temperatures, and when they occur

d) Find the avg. mean daily temperature

Any help on this would be appreciated. Please explain completely so that I fully understand and can do similar problems on my own. Thanks so much and 10 points to a best answer.

1 day ago

Answer 1

a) Trig functions are of the form:

y=C+Asin/cos(B(x-D) Where C=centerline, A=Amplitude, 2pi/B=period, and D=Phase Shift

So The Amplitude is A=27

b) Period =2pi/B=(2pi)/(2pi/365)=365=1 year

c) We're looking for Amplitude:

A=27, but that has to be added to, and subtracted from, the centerline, 64.

Highest=64+27=91degrees F

Lowest=64-27=37degrees F

d) The average is the centerline=64 degrees