Trig multi-part problem help 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.

Answer 1

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I am having problems getting

the right answer to this trigonometry question? it can be useful,

a) amplitude of the trigonom. part of the function f(x) is 27.

b)  period of the function is difference

(2Pi/365)(x + 145)=0  and

(2Pi/365)(x + 145)=2Pi

>x=-145    and

   x=220

we have period: 220-(-145)=365

c) Find the highest and lowest

mean daily temperatures, and when they occur:

highest: when cos()=1, (2Pi/365)(x + 145)=0  > x=-145

and  f(x) = 64 + 27=91 degrees Fahrenheit

lowest: when cos()=-1, (2Pi/365)(x + 145)=Pi  > x=75/2

and  f(x) = 64 - 27=37 degrees Fahrenheit

d) Find the avg. mean daily temperature:

definite integral  from 0 to 365 of the  f(x) = 23360,

and daily temperature =23360/365=64 degrees Fahrenheit