Find amplitude period and phase shift for
F(x)=-3cos(4x+n)+6
F(x) = -3cos(4(x+n/4))+6
So,
the amplitude is 3
the period is 2pi/4 = pi/2
the phase shift is -n/4
To find the amplitude, period, and phase shift of the function F(x) = -3cos(4x + n) + 6, we can break it down into its components.
Amplitude: The amplitude of a cosine function is the absolute value of the coefficient in front of the cosine term. In this case, the coefficient is -3, so the amplitude is | -3 | = 3.
Period: The period of a cosine function is the length of one complete cycle of the function. For a general cosine function f(x) = cos(bx), where b is the coefficient in front of x, the period is given by 2π / | b |. In this case, the coefficient in front of x is 4, so the period is 2π / | 4 | = 2π / 4 = π/2.
Phase Shift: The phase shift is the amount by which the graph of the function is translated horizontally. It is given by the expression -c / b, where c is the constant term (in this case, n) and b is the coefficient in front of x (in this case, 4). Since the constant term n is arbitrary and can take any value, we can say that the phase shift is -n / 4.
In summary:
Amplitude = 3
Period = π/2
Phase Shift = -n / 4, where n is any real number.