Write an equation of the cosine function with the given amplitude, period, phase shift, and vertical shift.
amplitude = 3, period = pi, phase shift = -3/4 pi, vertical shift = -3
Looks good to me.
I'd go with the +3cos(2θ + 3π/2)-3
since the cosine function is what is being given, not a flipped or shifted cosine.
The general equation for the cosine function is:
f(x) = A * cos(B(x - C)) + D
Where:
A = amplitude
B = 2π / period
C = phase shift
D = vertical shift
In this case:
amplitude = 3
period = π
phase shift = -3/4 π
vertical shift = -3
Substituting the given values into the equation, we have:
f(x) = 3 * cos((2π / π)(x - (-3/4π))) + (-3)
Simplifying further:
f(x) = 3 * cos(2(x + 3/4)) - 3
Therefore, the equation of the cosine function is:
f(x) = 3 * cos(2(x + 3/4)) - 3
To write the equation of the cosine function with the given amplitude, period, phase shift, and vertical shift, you can use the general form of the cosine function:
y = A * cos(B(x - C)) + D
where:
A is the amplitude
B is the reciprocal of the period
C is the phase shift
D is the vertical shift
In this case:
Amplitude (A) = 3
Period (P) = π
Reciprocal of period (B) = 1/P = 1/π
Phase Shift (C) = -3/4 π
Vertical Shift (D) = -3
Substituting these values into the general form, we get the equation:
y = 3 * cos((1/π)(x - (-3/4π))) - 3
Simplifying further, we have:
y = 3 * cos((1/π)(x + 3/4π)) - 3
This is the equation of the cosine function with the given properties.