Question

The function y=60+25sin(pi/6)t, where t is in months and t=0 corresponds to April 15, models the average high temperature in degrees Fahrenheit in Centerville.
b.) What is the maximum high temperature and when does this occur?

NOTE: I found the answer online, I just don't understand how to get there. It's July 15, 85 degrees.

Answer 1

Answer:

The maximum temperature will be of 85 degrees, on July 15.

Step-by-step explanation:

Sine function:

The sine function oscilates between -1 and 1, and it's maximum value is:

$\sin{(\frac{\pi}{2})} = 1$

y=60+25sin(pi/6)t

The maximum value will occur when $\sin{(\frac{\pi t}{6}}) = 1$, and it will be of 60 + 25 = 85 degrees.

When will it occur?

First we find the value of t for which the value inside the function sine is $\frac{\pi}{2}$. So

$\frac{\pi t}{6} = \frac{\pi}{2}$

$\frac{t}{6} = \frac{1}{2}$

$2t = 6$

$t = \frac{6}{2} = 3$

That is the number of months after April 15, which is 3 months. So July 15.