Houston, Texas has a latitude of 30°N. At this latitude, the position of the sun at sunrise can be modeled by D=27 sin( 2π/365 t - 1.3) where t is the time (in days) with t=1 representing January 1. In this model, D represents the number of degrees north of due east that the sun rises. What value of t corresponds to the first day that the sun is 20° north of due east at sunrise? Round your answer to the nearest integer.
[tex]D=27sin( \frac{2 \pi }{365} t-1.3)[/tex]

Respuesta :

[tex]D=27\sin{(\frac{2\pi}{365}t-1.3)}=27\sin{(0.9863t-74.48)}\\20=27\sin{(0.9863t-74.48)}}\\sin{(0.9863t-74.48)}=0.7407\\0.9863t-74.48=\arcsin0.7407=47.79\\0.9863t=47.79+74.48=122.3\\t=\frac{122.3}{0.9863}=124[/tex]

t = 124