Y=3sin(1/2 x+pi/6)please find amplitude period and phase shift

Question

asked May 25, 2023 3.3k views

1 Answer

Henry Keiter · Answer 1 · 2023-05-30T01:06:41+0000

The given function is

$y=3\sin ((1)/(2)x+(\pi)/(6))$

We have to use the following form

$a\sin (bx-c)+d$

Where the amplitude is a, the period is 2pi/b, and the phase shift is c/b. In the given function a = 3, b = 1/2, and c = pi/6.

$\begin{gathered} a=3 \\ T=(2\pi)/(b)=(2\pi)/((1)/(2))=4\pi \\ \theta=(c)/(b)=((\pi)/(6))/((1)/(2))=(2\pi)/(6)=(\pi)/(3) \end{gathered}$