Question

For the functions below state the amplitude, period, phase shift, and vertical translation of the graph for the sinusoid

Answer 1

see explanation

Explanation:

the standard form of the sine function is

y = asin(bx + c) + d

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

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

given

h(x) = - 3sin(x -
`(\pi )/(4)` ) + 2

with a = - 3, b = 1 , c = -
`(\pi )/(4)` , d = 2

Then

amplitude = | - 3 | = 3

period =
`(2\pi )/(1)` = 2π

phase shift = -
`(-(\pi )/(4) )/(1)` =
`(\pi )/(4)`

vertical shift = 2