The number of hours of daylight in City A is given by the fo

The number of hours of daylight in City A is given by the following equation, where x is the number of days after January 1. Within a year, when does City A have 12 hours of daylight? Give your answer in days after January 1. y = 3 sin [2 pi/365 (x - 79)] + 12 days (Use a comma to separate answers as needed. Round to the nearest integer as needed.)

Solution

we have given the number of hours of daylight in city A is given by y=3sin((2pi/365)(x-79))+12 and 12 hours day light

y=3sin((2pi/365)(x-79))+12

12 =3sin((2pi/365)(x-79))+12

3sin((2pi/365)(x-79))=0

sin((2pi/365)(x-79))=0

(2pi/365)(x-79)=arcsin(0)=0,when sin0=0,sin(pi)=0 and sin(2pi)=0

when arcsin(sin0) =0 and arcsin(sin(pi)) =0

(2pi/365)(x-79) =0

x=79

when arcsin(sin(pi)) =pi

(2pi/365)(x-79)=pi

x=(365/2)+79=261.5

x=261

when arcsin(sin(2pi)) =2pi

so x=79,261 days