Question

Given the trig function f(x) = -4 sin(3x - π) + 5, describe how it is transformed from the standard trig function f(x) = sin(x). That is, find the amplitude, period, phase shift, and vertical shift up.

Answer 1

see explanation

Explanation:

the equation of the sine function in general form is

y = a sin(bx + c) + d

where

amplitude = | a | , period =
`(2\pi )/(b)`

phase shift =
`(-c)/(b)` , vertical shift = d

given

y = - 4 sin(3x - π ) + 5

with a = - 4 , b = 3 , c = - π and d = 5 , then

amplitude = | - 4 | = 4

period =
`(2\pi )/(3)`

phase shift =
`(-(-\pi ))/(3)` =
`(\pi )/(3)`

vertical shift = + 5 ( that is a vertical shift )