Using the same equation from problem 1, what is the average temperature in Atlanta, GA, for the month of June?
equation from #1 is
y = 18.25 sin(pi/6 t - 2.09) + 61.15
where t is the time in months and January is t = 1.
Y = 18.25sin(t*pi/6 - 2.09) + 61.15.
Y = 18.25*sin(6*3.14/6 - 2.09) + 61.15,
Y = 18.25*sin(3.14 - 2.09) + 61.15,
Y = 18.25*sin(1.052) + 61.15,
Convert to degrees:
Y = 18.25*sin(1.052*57.3deg/rad) + 61.15,
Y = 18.25*sin(60.28) + 61.15,
Y = 16 + 61.15 = 77.15deg in June.
To find the average temperature in Atlanta, GA, for the month of June using the equation y = 18.25 sin(pi/6 t - 2.09) + 61.15, we need to substitute the values of t that correspond to June into the equation and calculate the average.
First, we need to determine the value of t that corresponds to June. Assuming January is t = 1, we can use the fact that June is the 6th month of the year. So, June would correspond to t = 6.
Substituting t = 6 into the equation, we get:
y = 18.25 sin(pi/6 * 6 - 2.09) + 61.15
Simplifying the expression inside the sine function:
y = 18.25 sin(pi - 2.09) + 61.15
y = 18.25 sin(0.12) + 61.15
Using a calculator to evaluate sin(0.12) and rounding to the appropriate number of decimal places:
y ≈ 18.25 * 0.119 + 61.15
y ≈ 2.18 + 61.15
y ≈ 63.33
Therefore, the average temperature in Atlanta, GA, for the month of June is approximately 63.33 degrees.