The temperature in your house is controlled by a thermostat. The temperatures will vary according to the sinusoidal function: f(x)=6sin(Pi/12(x-15))+19 , where f(x) represents the temperature in degrees Celsius (°C) and x is hours since midnight. What is the temperature of your house at 3:00 p.m.?
3 pm is 15 hours after midnight.
So, plug in x=15 and you have
f(15)=6sin(Pi/12(15-15))+19 = 19
Thanks
To find the temperature of your house at 3:00 p.m., we need to substitute the value of x which represents hours since midnight into the given function.
Since 3:00 p.m. is 15 hours after midnight, we can substitute x = 15 into the function:
f(x) = 6sin((π/12)(x - 15)) + 19
f(15) = 6sin((π/12)(15 - 15)) + 19
Here, sin(0) = 0, so the equation simplifies to:
f(15) = 6(0) + 19
Therefore, the temperature in your house at 3:00 p.m. is:
f(15) = 19°C.