Write an equation of a cosine function with Amplitude=4, Period=pi/2, and Phase Shift=-pi?
To write the equation of a cosine function with the given amplitude, period, and phase shift, we can use the general form of a cosine function:
y = A * cos(B(x - C)) + D
Where:
A is the amplitude
B is the frequency (or the reciprocal of the period)
C is the phase shift
D is the vertical shift
For the given parameters:
Amplitude = 4
Period = π/2
Phase Shift = -π
First, we need to determine the values of A, B, C, and D:
The amplitude (A) is given as 4.
A = 4
The period (T) is the reciprocal of the frequency (B). The given period is π/2, so the frequency is:
T = π/2 = 2π / (2π/2) = 2π / B
B = 2π / T = 2π / (π/2) = 4
The phase shift (C) is given as -π.
C = -π
The vertical shift (D) is not given, so we assume there is no vertical shift (D = 0).
D = 0
Now, we can substitute the values into the general form equation:
y = 4 * cos(4(x + π)) + 0
Therefore, the equation of the cosine function with the given amplitude, period, and phase shift is:
y = 4 * cos(4(x + π))