Answer
$T = a~sin~[b(x-d)]+c$
$a~~$ is the amplitude of the sine curve
$b~~$ is the angular frequency $\omega$
$c~~$ is the vertical translation of the sine curve.
$d~~$ is the horizontal translation of the sine curve toward the right.
Work Step by Step
$T = a~sin~[b(x-d)]+c$
In part (b), we modeled the sine curve with this function:
$T = 25.5~sin~[0.5236(x-5.429)]+49$
$a = 25.5~~$ is the amplitude of the sine curve
$b = 0.5236$ is the angular frequency and it is related to the period $P$ as follows:
$b = \frac{2\pi}{P}$
$c= 49$
$c~~$ is the vertical translation of the sine curve.
$d = 5.429$
$d~~$ is the horizontal translation of the sine curve toward the right.
