Answer:
(a). The sinusoidal function is
-14×cos((π/12)×(t-2))+55
(b). The temperature of 48 ° first occurs at 6.00 a.m.
Step-by-step explanation:
To solve the question, we note that an example of a sinusoidal function is a cosine function
a×cos×(2π/k)t+b = Temperature
For a 24 hour period, the sinusoidal function becomes
2π/k =24 or k = π/12 and
a = (69 - 41)/2 = 14 also b = 69 -14 = 55
Therefore the sinusoidal function becomes
14×cos((π/12)×t)+55 = Temperature at a particular time of day
checking we have
at 6 a.m. 14×cos(π/2) +55 = 55 ° okay
However the average temperature supposed to occur at 8 a.m.
Therefore we have time adjustment by 2 hours hence
Our equation becomes
-14×cos((π/12)×(t-2))+55 = Temperature
Therefore at 8 a.m. we have
-14×cos((π/12)×(8-2))+55 = 55 ° = average temperature
And
(b) For 48 °, we have
-14×cos((π/12)×(t-2))+55 = 48
or t = 6 a.m.
