What is the amplitude, period, and phase shift of f(x) = -4 sin(2x + π) - 5?

Solution:

f(x) = -4 sin(2x + π) - 5

The function is in the form f(x) = λsin(μx - Φ) + β

Where: |λ| = amplitude

2π/μ = period

Φ/μ = phase shift

So the amplitude is: |-4| = 4

The period is: 2π/2 = π

And the phase shift is: π/2

We may also note that β is the vertical shift of the function and it shift by -5 up or 5 down

What is the amplitude, period, and phase shift of f(x) = -4 sin(2x + π) - 5?

Summary:

The amplitude, period, and phase shift of f(x) = -4 sin(2x + π) - 5 are 4, π and π/2 respectively.