f(x) = -cos(3x + pi). Find the amplitude, period, and phase shift of the function.
f(x) = -cos(3x + pi)
= -1cos 3(x+π/3)
ampl = 1
period = 2π/3
phase shift -π/3 to the left
To find the amplitude, period, and phase shift of the function f(x) = -cos(3x + π), let's break it down step-by-step:
1. Amplitude: The amplitude of a cosine function is the absolute value of the coefficient of the cosine term. In this case, the coefficient is -1, so the amplitude is 1.
2. Period: The period of a cosine function is 2π divided by the coefficient of x in the argument of cosine. In this case, the coefficient is 3, so the period is 2π/3.
3. Phase Shift: The phase shift of a cosine function is found by setting the argument of cosine (3x + π) equal to zero and solving for x. In this case, set 3x + π = 0:
3x + π = 0
3x = -π
x = -π/3
The phase shift is -π/3.
So, the amplitude is 1, the period is 2π/3, and the phase shift is -π/3 for the function f(x) = -cos(3x + π).