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

1313 hours of daylight? Give your answer in days after January 1.

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

Solution

13 hours of daylight

=>3 sin[(2_/365)(x-79)] +12 =13

=>3 sin[(2_/365)(x-79)] =13-12

=>3 sin[(2_/365)(x-79)] =1

=>sin[(2_/365)(x-79)] =1_/3

=>[(2_/365)(x-79)] =sin^-1(1_/3) ,[(2_/365)(x-79)] =-sin^-1(1_/3)

=>(x-79) =(365_/2)sin^-1(1_/3) ,(x-79) =(365_/2) - (365_/2)sin^-1(1_/3)

=>x =79+((365_/2)sin^-1(1_/3)),x =79+(365_/2)  - ((365_/2)sin^-1(1_/3))

=>x =241.758 ,x =98.74

13 hours of daylight on 242^nd day and 99^th day after january 1

13 hours of daylight on 243^rd day and 100^th day of the calender year

i.e, August31^st, April10^th