Amplitude, period, and phase shift of sine and cosine functions

Question

asked Aug 4, 2023 216k views

1 Answer

Wholeman · Answer 1 · 2023-08-10T13:02:57+0000

We are given that

$y=-2+2\cos (2x-(\pi)/(3))$

Note: Given the cosine function

$y=a\cos (bx-c)+d$

then

$\begin{gathered} Amplitude=a \\ Period=(2\pi)/(b) \\ PhaseShift=(c)/(b) \\ VerticalShift=d \end{gathered}$

Comparing the question with what is written in the note

We have

$\begin{gathered} a=2 \\ b=2 \\ c=(\pi)/(3) \\ d=-2 \end{gathered}$

We want to find

(a). Amplitude

From the given question, the amplitude (a) is

$\begin{gathered} a=2 \\ Amplitude=2 \end{gathered}$

(b).Period

From the given question, the period is

$\begin{gathered} Period=(2\pi)/(b) \\ Period=(2\pi)/(2) \\ Period=\pi \end{gathered}$

(c). Phase Shift

From the given question, the phase shift is

$\begin{gathered} PhaseShift=(c)/(b) \\ PhaseShift=(\pi)/(3)*(1)/(2) \\ PhaseShift=(\pi)/(6) \end{gathered}$