The average temperature, in °F, for Atlanta, GA is modeled by the sinusoidal function
y = 18.25 sin(pi/6 t - 2.09) + 61.15
where t is the time in months and January is t = 1.
What is the average temperature for the month of February?
How do I do this problem ?
Please Help
since Feb ---> t = 2
sub that in, make sure your calculator is set to radians
y = 18.25 sin ((π/6)(2)-2.09) + 61.15
= 45.39
make sure to follow the order of operation.
Thankyou!
To find the average temperature for the month of February, you need to substitute the value of t for February into the given equation and calculate the corresponding value of y.
In the equation y = 18.25 sin(pi/6 t - 2.09) + 61.15, t represents time in months and January is t = 1. So, you need to find the value of t for February.
Since January is t = 1, February will be the second month, so t = 2.
Now, plug t = 2 into the equation:
y = 18.25 sin(pi/6 * 2 - 2.09) + 61.15
Simplify the expression inside the sine function:
y = 18.25 sin(pi/3 - 2.09) + 61.15
Now, calculate the sine of (pi/3 - 2.09) using a calculator:
sin(pi/3 - 2.09) ≈ 0.347
Substitute this value back into the equation:
y = 18.25 * 0.347 + 61.15
Now, calculate this expression:
y ≈ 6.335 + 61.15
y ≈ 67.485
Therefore, the average temperature for the month of February in Atlanta, GA is approximately 67.485 degrees Fahrenheit.