Question

The temperature in Sam's home varies sinusoidal over time. Given the equation T = 4 cos(30(t − 8)) + 16 describes the temperature of the house in degrees celsius in terms of the number of hours since 12 midnight.

Answer 1

Answer:

The temperature is: 14.5 degrees

Step-by-step explanation:

Given

$T = 4 \cos(30(t - 8)) + 16$

Required

The temperature at 4:15

We have:

$t = 4:15$

Convert to hours

$t = 4+\frac{15}{60}$

$t = 4+0.25$

$t = 4.25$

So:

$T = 4 \cos(30(t - 8)) + 16$

$T = 4 \cos(30(4.25 - 8)) + 16$

$T = 4 \cos(30(-3.75)) + 16$

Open bracket

$T = 4 \cos(-112.5) + 16$

$T = 4 *-0.3826 + 16$

$T = -1.5304 + 16$

$T = 14.4696$

Approximate

$T = 14.5^o$