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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.

Sagot :

MrRoyal

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]

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