Question

The first sunrise in the United States each day is observed from Cadillac Mountain on Mount Desert Island in Maine. The time of the sunrise can be modeled by t(m) = 1.665 sin (m + 3) + 5.485, where t is hours after midnight and m is the number of months after January 1. When does the sunrise at 6:00 A.M.?

Answer 1

First we will subsitute 6 for variable "t", Then solve for variable "m" using Algebra;
\[6 = 1.665\sin \frac{ \Pi }{ 6 }(m+ 3)+ 5.485\]
Now, you need to isolate the sine term;
\[\frac{ 6-5.485 }{ 1.665 }=\sin \frac{ \Pi }{ 6 }(m+3)\]
Now, Imply the Inverse Sine
\[\sin^{-1} (0.3093)=\frac{ \Pi }{ 6 }(m+3)\]
Sine is positive in Quadrants I and II.
\[\sin^{-1} (0.3039)=\frac{ \Pi }{ 6 }(m+3)\]
\[0.314=\frac{ \Pi }{ 6} (m+ 3)\]
\[(\frac{ 6 }{ \Pi})0.314=m+3\]
\[-2.400=m\]
&
\[2.400=m\]

Answer 2

𝘐 𝘩𝘰𝘱𝘦 𝘵𝘩𝘢𝘵 𝘩𝘦𝘭𝘱𝘦𝘥, 𝘭𝘦𝘵 𝘮𝘦 𝘬𝘯𝘰𝘸 𝘪𝘧 𝘺𝘰𝘶 𝘯𝘦𝘦𝘥 𝘢𝘯𝘺𝘵𝘩𝘪𝘯𝘨 𝘦𝘭𝘴𝘦 𝘣𝘺 𝘤𝘰𝘯𝘵𝘢𝘤𝘵𝘪𝘯𝘨 𝘮𝘦.

ℂ𝕣𝕖𝕖𝕕