4. Write the equation of the cosine function with an amplitude of 1/3, a period of 2pi, and a phase shift of 3pi/2.
I got 1/3COS(1/2x-3pi), but I really do not think that is correct D: any tips or advice?
why the half? cosx already has a period of 2pi.
1/3 cos(x-3pi/2)
To write the equation of a cosine function with the given amplitude, period, and phase shift, you can use the following general form:
f(x) = A * cos(B(x - C))
The amplitude is the absolute value of A, the period is the value of 2pi divided by B, and the phase shift is C.
In your case, the given amplitude is 1/3, the period is 2pi, and the phase shift is 3pi/2.
First, let's determine A. The amplitude is already given as 1/3, so A = 1/3.
Next, let's find B. The period is 2pi, which means B = 2pi / period. In this case, B = 2pi / 2pi = 1.
Lastly, let's determine C. The phase shift is 3pi/2, so C = phase shift. Therefore, C = 3pi/2.
Now, we can substitute the values of A, B, and C into the general form and write the equation of the cosine function:
f(x) = (1/3) * cos(x - 3pi/2)
So, the correct equation of the cosine function with an amplitude of 1/3, a period of 2pi, and a phase shift of 3pi/2 is:
f(x) = (1/3) * cos(x - 3pi/2)