The temperature in your house is controlled by a thermostat. The temperatures will vary according to the sinusoidal function: f(x)=5sin(pi/12)*(x-11)+19 where f(x) represents the temperature in degrees Celsius (°C) and x is hours since midnight. What is the maximum temperature of your house?
a.)5deg Celcius
b.)16 deg celcius
c.)17 deg celcius
d.)25 deg celcius
I thought that 23 hours was the maximum hours since midnight, but I got a strange answer when I plugged that in for x. What am I doing wrong? Thanks!
The max temperature is 26º C
23 is the maximum hours, but you want the maximum temperature.
sin(x) has a maximum of 1
5sin(x) has a max of 5
5sin(x)+19 has a max of 24
It appears there is a typo, since 24 is not a choice.
To find the maximum temperature of your house, we need to find the maximum value of the sinusoidal function f(x). The maximum value occurs when the sine function reaches its maximum value of 1.
The equation of the sinusoidal function is f(x) = 5sin(pi/12)(x - 11) + 19.
To find the maximum value of f(x), we need to determine the maximum value of the sine term, which is sin(pi/12)(x - 11). Since the sine function oscillates between -1 and 1, we set sin(pi/12)(x - 11) equal to 1.
1 = sin(pi/12)(x - 11)
To solve for x, we isolate x by dividing both sides of the equation by sin(pi/12):
1/sin(pi/12) = x - 11
Now, let's calculate the value of 1/sin(pi/12):
1/sin(pi/12) ≈ 25.88
Adding 11 to both sides of the equation, we get:
25.88 + 11 ≈ 36.88
So, the maximum value of x is approximately 36.88 hours since midnight.
However, you mentioned that 23 hours since midnight resulted in a strange answer when plugged into the equation. This could be due to a typo or an error in the equation you provided. Please double-check the equation to ensure its accuracy.