Question

What is the amplitude, period, and phase shift of f(x) = −2 sin(3x − π) − 1?

Answer 1

see explanation

Explanation:

The standard form of the sine wave function is

y = a sin (bx + c) + d

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

phase shift = -
`(c)/(b)` and d is the vertical shift

Here a = - 2, b = 3 and c = - π

Hence

amplitude = | - 2 | = 2

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

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