The normal average daily temperature in degrees Fahrenheit for a city is given by $51 - 23 \cos \frac { 5 \pi ( t - 33 ) } { 365 }$ where t is the time in days, with $t = 1$ corresponding to January 1. Find the warmest day.
A)March 17
B)March 16
C)April 17
D)April 16
E)April 15

Question

Quizplus · Accepted Answer

The warmest day occurs when the cosine function, $\cos \frac { 5 \pi ( t - 33 ) } { 365 }$, is at its minimum value, because the cosine function is subtracted from 51. The minimum value of cosine is -1, which occurs when its argument equals an odd multiple of $\pi$. Setting the argument equal to $\pi$ (the first odd multiple) gives $\frac { 5 \pi ( t - 33 ) } { 365 } = \pi$, solving for $t$ gives $t = 33 + \frac{365}{5} = 33 + 73 = 106$. Day 106 of the year is April 16, making it the warmest day.

The Normal Average Daily Temperature in Degrees Fahrenheit for a City