Answer:
The temperature is: 14.5 degrees
Step-by-step explanation:
Given
[tex]T = 4 \cos(30(t - 8)) + 16[/tex]
Required
The temperature at 4:15
We have:
[tex]t = 4:15[/tex]
Convert to hours
[tex]t = 4+\frac{15}{60}[/tex]
[tex]t = 4+0.25[/tex]
[tex]t = 4.25[/tex]
So:
[tex]T = 4 \cos(30(t - 8)) + 16[/tex]
[tex]T = 4 \cos(30(4.25 - 8)) + 16[/tex]
[tex]T = 4 \cos(30(-3.75)) + 16[/tex]
Open bracket
[tex]T = 4 \cos(-112.5) + 16[/tex]
[tex]T = 4 *-0.3826 + 16[/tex]
[tex]T = -1.5304 + 16[/tex]
[tex]T = 14.4696[/tex]
Approximate
[tex]T = 14.5^o[/tex]
