Question

Find the amplitude, period, vertical translation horizontal translation and phase

Answer 1

we have that

The general equation is of the form

`y=Asin[B(x+C)]+D`

where

A is the amplitude

period is 2π/B

phase shift is C

vertical shift is D

In this problem we have

`y=(5)/(2)-(1)/(2)sin(3x+pi)`

Rewrite the given expression

`y=-(1)/(2)s\imaginaryI n[3(x+(p\imaginaryI)/(3))]+(5)/(2)\text{ -----> equivalent expression}`

therefore

Amplitude is 1/2

Period=2pi/3

phase shift is pi/3 (to the left)

vertical shift is 5/2 (up)