Final answer:
To find the second time after the hottest day of the year that the daily high temperature is 20 degrees Celsius, you need to solve the equation T(t) = 20. This involves finding the inverse cosine of a specific value, setting up an equation, and adding one year to the solution. After performing these steps, you can find the value of t that corresponds to the second time.
Step-by-step explanation:
To find the second time after the hottest day of the year that the daily high temperature is 20 degrees Celsius, we need to solve the equation T(t) = 20. We can rewrite this equation as 7.5cos(2π/365t) + 21.5 = 20. Subtracting 21.5 from both sides gives us 7.5cos(2π/365t) = -1.5. Dividing both sides by 7.5 and simplifying further, we have cos(2π/365t) = -0.2. To find the second time, we need to find the value of t that satisfies this equation.
To find the value of t, we need to use the inverse cosine function (also known as arccosine). The inverse cosine function (cos^(-1)) gives us the angle whose cosine is a specific value. In this case, we want to find t such that cos(2π/365t) = -0.2. We can use a calculator or math software to find the inverse cosine of -0.2. Let's assume the inverse cosine of -0.2 is x.
Now we can set up an equation: 2π/365t = x. Solving for t, we get t = (365x)/(2π). However, we need to find the second time after the hottest day, so we need to find the value of t that satisfies the equation after adding one year (365 days) to the original value. Therefore, the second time after the hottest day of the year that the daily high temperature is 20 degrees Celsius is t = (365x)/(2π) + 365.