Question

Outside temperature over a day can be modeled as a sinusoidal function. Suppose you know the temperature is 45 degrees at midnight and the high and low temperature during the day are 50 and 40 degrees, respectively. Assuming t is the number of hours since midnight, find an equation for the temperature, D, in terms of t.

Answer 1

Answer:

so  equation for the temperature in terms of t is D = 5 sin $\pi$ / 12 (t) + 45

Step-by-step explanation:

Given data

temperature = 45 degrees

high temperature = 50 degrees

low temperature = 40 degrees

to find out

an equation for the temperature in terms of t

solution

first we find the amplitude i.e.

Amplitude (A) = ( high temperature - low temperature )  / 2

Amplitude (A) = (50 - 40)  / 2

Amplitude (A)  = 5

here we know in a day 24 hours so

2$\pi$ /K = 24

K = $\pi$ / 12

so we have temperature equation is

temperature D = amplitude sinK (t) + avg temperature midnight

D = 5 sin $\pi$ / 12 (t) + 45

so  equation for the temperature in terms of t is D = 5 sin $\pi$ / 12 (t) + 45