The function Sm940 cospi6m1578 models the average monthly te

The function S(m)=9.40 cos(pi/6(m-1))+57.8 models the average monthly temperatures in degrees Fahrenheit in Sydney, Australia during the mth month of the year. Solve 53.1=9.40 cos(pi/6(m-1))+57.8 on the interval [1,12].

Solution

Solve : 53.1=9.40 cos(pi/6(m-1))+57.8 on the interval [1,12].

-4.7/9.40 = cos(pi/6(m-1))

-0.5 = cospi/6(m-1))

2pi/3 = pi/(6(m-1)

6m -6 = 3/2

6m-6 = 1.5

6m = 7.5

m = 7.5/6 = 1.25

Now period of this function is 2pi/ pi/6 = 12

So, only solution is m= 1.25 month which means month of February