amplitude, period, frequency, and the like....?

Question

f(x)=4sin(3x+pi)

Amplitude: 4
Period: ?

I had put 2pi/3 + pi = 5pi/3
^^how i got that i have no idea....but anyways, my teacher found it necessary to circle the 2pi/3 part....any insights? thanks :-)

Answer 1

How often does your 3x pass through 2 pi?

3x = 2 pi
x = 2 pi / 3

The period is 2 pi / 3

The extra pi is just a shift to the left.

Answer 2

f(x) = Asin(ωx - Ф)
Amplitude = A
Period = (2pi)/ω
Parameter(phase angle) = Ф
Frequency = ω

f(x) = 4sin(3x + pi)

period

period = (2pi)/3 or (2pi/3)

Amplitude : 4
Period : ((2pi)/3)
Frequency : 3

as for your

(2pi/3) + pi = (2pi/3) + (3pi/3) = (2pi + 3pi)/3 = (5pi/3)

the reason she tells you to circle it, which i'm hoping she means () and not an actual circle, is because if you put 2pi/3 + pi, then some people may think you mean (2pi)/(3 + pi) instead of (2pi/3) + pi