The average temperature, in °F, of City B is given by the equation:y=19.5sin(pi/6t-2.06)+62 , where t is the time in months and t = 1 corresponds to January. What is the average temperature in April? Round your answer to the nearest hundredth.
in April t = 4
y = 19.5 sin (4 pi/6 -2.06) + 62
y = 62 + 19.5 sin (.0344)
y = 62 + 19.5 sin (1.97) my calculator does degrees
y = 62.67
Thankyouuu!
To find the average temperature in April, we need to determine the value of "t" that corresponds to the month of April.
We know that t = 1 corresponds to January, so we need to figure out how many months have passed from January to April. Since there are 12 months in a year, April is the fourth month.
Therefore, t = 4 corresponds to April.
Now that we have determined the value of "t," we can plug it into the equation:
y = 19.5sin(pi/6t - 2.06) + 62
y = 19.5sin(pi/6 * 4 - 2.06) + 62
Simplifying further:
y = 19.5sin(2pi/3 - 2.06) + 62
To calculate this, we need to convert the angles from radians to degrees.
2pi/3 ≈ 120 degrees
Now we can plug in the value and calculate:
y = 19.5sin(120 - 2.06) + 62
Using a scientific calculator, we find:
y ≈ 32.67
Therefore, the average temperature in April is approximately 32.67°F.