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

The temperature is: 14.5 degrees

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+(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`