The length of a day in Philadelphia, Pennsylvania, is given by the sinusoidal function, f(t), which represents the number of hours of daylight t days into the year: f(x)=11+2.2sin(2pi/365)t-1.25).How many hours of daylight are there on the twelfth day of the year? Round the answer to the nearest tenth.

Question

a) 9.1 hours
b)9.9 hours
c)12.0 hours
d) 13.4 hours

I plugged in 12 for t in the equation, but came up with 11.007 as my answer. Why am I getting an answer that is not one of the choices?? Am I doing something wrong?? Thanks SO much!

Answer 1

The twelfth day of the year mean t = 12

Now you must put t = 12 into your equation.

( 2 pi / 365 ) t - 1.25 ) =

( 2 * 3.14159216535 / 365 ) * 12 - 1.25 =

( 6.283185307 / 365 ) * 12 - 1.25 =

0.01721420632 * 12 - 1.25 =

0.20657047584 - 1.25 =

- 1.04342952416

Now take calculator ( set angle on radians )

sin ( 2 pi /365 ) t - 1.25 ) =

sin ( - 1.04342952416 ) =

- 0.8641352468

2.2 sin ( 2 pi / 365 ) t - 1.25 ) =

2.2 * ( - 0.8641352468 ) =

- 1.90109754296

11 + sin ( 2 pi /365 ) t - 1.25) =

11 + ( - 1.90109754296 ) =

11 - 1.90109754296 =

9.09890245704 = 9.1 rounded to the nearest tenth

Answer a