Question

The average daily high temperature in Seattle is modeled by the function T = –15 cos(πm/6)+ 61, where T is the temperature in °F, and m is the number of months since the beginning of the year. What is the value of m when the average daily high temperature T is 76°F

Answer 1

Answer:

$m = 6$

Step-by-step explanation:

$T = -15cos(\frac{\pi m}{6}) +61$

$76 = -15cos(\frac{\pi m}{6}) +61$

$76-61 = -15cos(\frac{\pi m}{6})$

$15 = -15cos(\frac{\pi m}{6})$

$\frac{15}{-15} = cos(\frac{\pi m}{6})$

$-1 = cos(\frac{\pi m}{6})$

$cos^{-1}( -1) = \frac{\pi m}{6}$

$\pi = \frac{\pi m}{6}$

$6\pi = \pi m$

$m = 6$