Question

The temperature during a day can be modeled by a sinusoid. Answer the following question given that the low temperature of 53 degrees occurs at 4 AM and the high temperature for the day is 99 degrees. Find the temperature, to the nearest degree, at 8 AM.

Answer 1

Answer:

73 degrees

Step-by-step explanation:

Given that the temperature during a day can be modeled by a sinusoid.

At 4 am. lowest = 53 deg and at 4 pm highest = 99 deg

Amplitude = (99-53)/2 = 23

Mean temp = 76 deg

If 4 am is taken as t =0 then we have middle temp = 46 degrees at 10 a.m.

Hence equation would be of the form

T(t) =23 sin (pi t/12)+53 where T is the temperature and t is time in hours from 4 a.m.

At 8 am t =4

So T(4) = 23 sin pi/3 +53  = 19.92+53  =72.92

Nearly 73 degrees