Determine the period p,the amplitude b,the phase shift d,and the vertical shift a of the given trigonometric function f(t). $$f ( t ) = 1.5 + 5.5 \sin \left[ \frac { \pi } { 3 } ( t - 1 ) \right]$$
A) $p = 6 , b = - 5.5 , d = - 1 , a = 1.5$
B) $p = 3 , b = 1.5 , d = 1 , a = 5.5$
C) $p = 6 , b = 5.5 , d = 1 , a = 1.5$
D) $p = 6 , b = 1.5 , d = 1 , a = 5.5$

Question

Quizplus · Accepted Answer

The general form of a sine function is $f(t) = a + b \sin[c(t - d)]$, where $a$ is the vertical shift, $b$ is the amplitude, $c$ is related to the period by $p = \frac{2\pi}{c}$, and $d$ is the phase shift. For $f(t) = 1.5 + 5.5 \sin\left[\frac{\pi}{3}(t - 1)\right]$, $a = 1.5$, $b = 5.5$, $c = \frac{\pi}{3}$ so $p = \frac{2\pi}{\pi/3} = 6$, and $d = 1$.

Determine the Period P,the Amplitude B,the Phase Shift D,and the Vertical