# 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 midnight, find an equation for the temperature, D, in terms of t.

• So I am pretty sure the equation would start y=25sin(x) because 25 is the difference between the highest and lowest temperature
• In a sine equation the point at 3pi/2 is the lowest, so I think we have to move the graph over so that 5 is the lowest point??? Because the lowest temp happens at 5 hours past midnight. That doesn't really make sense but I'm not sure how to go about this problem.

1. 👍 0
2. 👎 0
3. 👁 868
1. 2 A = 87-63 = 24
so A = 12 degrees
average = (87+63)/2 = 75
so
D = 75 + 12 sin (2 pi t/24 - p)
where p is the phase to give the right temp when t = 5
when t = 5
sin (2 pi 5/24 - p) = -1

or 5 pi/12 - p = -pi/2
p = 6 pi/12 + 5 pi/12 = 11 pi/12

so
D = 75 + 12 sin ( pi t/12 - 11 pi/12)
or
D = 75 + 12 sin [ pi/12(t-11) ]

1. 👍 0
2. 👎 0
posted by Damon

## Similar Questions

1. ### Trig

Outside temperature over a day can be modelled as a sinusoidal function. Suppose you know the high temperature for the day is 51 degrees and the low temperature of 39 degrees occurs at 3 AM. Assuming t is the number of hours since

asked by Brody on December 11, 2019
2. ### 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

asked by marie darling on March 26, 2013
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. ### 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
5. ### 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
6. ### Precalculus

Outside temperature over a day can be modeled as a sinusoidal function. Suppose you know the temperature is 55 degrees at midnight and the high and low temperature during the day are 62 and 48 degrees, respectively. Assuming t is

asked by HAHA on September 15, 2019
7. ### 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
8. ### 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
9. ### 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
10. ### 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

More Similar Questions