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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.


D=27sin( (2 \pi )/(365) t-1.3)

1 Answer

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D=27\sin{((2\pi)/(365)t-1.3)}=27sin((0.9863t-74.48))\\20=27sin((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=(122.3)/(0.9863)=124

t = 124
User Zohaib Ijaz
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