Find the temperature

Question

The temperature during a day can be modeled by a sinusoid. Answer the following question given that the low temperature of 62 degrees occurs at 4 AM and the high temperature for the day is 88 degrees.

Find the temperature, to the nearest degree, at 9 AM.

Answer 1

Want to model this on:

T(x) = Asin(B(x+C))+D where x=[0,24]

Range of sine = [-1,1]

-A+D = 62

A+D = 88

D=75

A=13

B=2π/24 = π/12

Want B(x+C) = 3π/2 when x = 4

π/12(4+C) = 3π/2

4+C=18

C=14

T(x)=13sin(π(x+14)/12)+75

T(9) = 13sin(23π/12)+75 ≈71.63° ≈ 72°