Question

Q.1 Outside temperature over a day can be modeled as a sinusoidal function. Suppose you know the high temperature of 83 degrees occurs at 6 PM and the average temperature for the day is 65 degrees. Find the temperature, to the nearest degree, at 10 AM. (Answer: degrees)

Q.2 Outside temperature over a day can be modeled as a sinusoidal function. Suppose you know the temperature varies between 60 and 90 degrees during the day and the average daily temperature first occurs at 10 AM. How many hours after midnight, to two decimal places, does the temperature first reach 71 degrees? (Answer: hours)

Please answer all of the questions!

Answer 1

1.

with the given details in the problem

Midline (C) is the average is 65 degrees
Amplitude (A) is 83-65=18;
Period = 24 hours;
ω=2π/24;
α=10;

  therefore the temperature is 64.17 degrees
2.

With the information given in this problem,
Midline (C) is the average calculated as: (60+90)/2=75;
Amplitude (A) is 90-75= 15;
Period = 24 hours;
ω=2π/24;
α=10;

Substituting in the equation,
y=15∗sin[2π/24(x−10)]+75

Solving this equation for y=71 gives the value of x as 9.98.

Thus, the temperature first reaches 71 degrees about 9.98 hours after midnight.