precalculus

Outside temperature over a day can be modelled as a sinusoidal function. Suppose you know the temperature is 80 degrees at midnight and the high and low temperature during the day are 90 and 70 degrees, respectively. Assuming t is the number of hours since midnight, find an equation for the temperature, D, in terms of t.

  1. 👍 0
  2. 👎 0
  3. 👁 3,094
  1. let's pick a sine function

    the range is 9-70 = 20
    so a = 10
    we know that the period is 24 hrs
    so 2π/k=24
    24k = 2π
    k = π/12

    so far we have:
    D = 10 sin(π/12)(t) + 80
    giving us a range from 70 to 90

    But obviously the temp after midnight would decrease, whereas our function has it increasing to 90 when t = 6 (6:00 am)
    We could do a phase shift, or more simply, just flip the function to
    D = -10sin(π/12)t + 80

    check some values
    t = 0 , D = -10sin0 + 80 = 80 , ok
    t=6 , (6:00 am) D = -10 sin (π/2) + 80 = 70 , ok
    t = 12 (noon), D = -10 sin π + 80 = 80 , ok
    t = 18 , (6:00 pm) , D = -10sin 3π/2 + 80 = 90

    all looks good

    1. 👍 2
    2. 👎 0
    posted by Reiny
  2. Outside temperature over a day can be modeled as a sinusoidal function. Suppose you know the high temperature of 52 degrees occurs at 6 PM and the average temperature for the day is 45 degrees. Find the temperature, to the nearest degree, at 8 AM.

    1. 👍 0
    2. 👎 1

Respond to this Question

First Name

Your Response

Similar Questions

  1. Math

    Outside temperature over a day can be modelled as a sinusoidal function. Suppose you know the high temperature for the day is 87 degrees and the low temperature of 63 degrees occurs at 5 AM. Assuming t is the number of hours since

    asked by Holly on September 2, 2014
  2. math-precalculus

    Outside temperature over a day can be modeled as a sinusoidal function. Suppose you know the temperature varies between 73 and 87 degrees during the day and the average daily temperature first occurs at 8 AM. How many hours after

    asked by j on April 27, 2017
  3. math

    Outside temperature over a day can be modeled as a sinusoidal function. Suppose you know the temperature varies between 55 and 85 degrees during the day and the average daily temperature first occurs at 10 AM. How many hours after

    asked by pika on July 22, 2019
  4. Trigonometry

    Outside temperature over a day can be modeled as a sinusoidal function. Suppose you know the high temperature of 95 degrees occurs at 3 PM and the average temperature for the day is 80 degrees. Find the temperature, to the nearest

    asked by Julie on November 1, 2016
  5. Math

    The height of the tide in a given location on a given day is modelled using the sinusoidal function h(t)=5 sin (30(t-5))+7. a) What time is high tide? What time is low tide?

    asked by Emily on January 10, 2011
  6. Trigonometry

    Can someone please explain this to me?? I'm really stuck on it. First of all, i don't know if I should use cosine or sine for the function because it only says to make a sinusoidal function that models the data, and a sinusoidal

    asked by Geni on February 13, 2018
  7. math

    The temperature in degree celcius in a factory during the course of a working day from 6am to 10pm can be modelled by the function H(t)=18+6sin(pit/8-5pi/4)for 6

    asked by HApida on May 7, 2010
  8. Math

    the temperature in degree celcius in a factory during the course of a working day from 6am to 10pm, can be modelled by the function H(t)=18+6sin(pi/8-5pi/4)for6< t < 22 - - where t is the time in hours on 24 hour clock. what are

    asked by pawan puri on April 27, 2010
  9. Calculus

    How would you begin this problem? On a standard summer day in upstate New York, the temperature outside can be modeled using the sinusoidal equation O(t) = 11 cos (pi/12 t) + 71, where t represents the number of hours since the

    asked by Jillian on August 22, 2012
  10. Algebra

    Stella is recording temperatures every day for 5 days. On the first day, Stella recorded a temperature of 0 degrees Farenheit. A. On the second day, the temperature was 3 degrees Fahrenheit above the temperature on the first day.

    asked by Ms. Stephie on September 18, 2014

More Similar Questions