find the amplitude, period and the phase shift

Question

find the amplitude, period and phase shift of 

y=2sin ((2/3)x-pi/6)

Answer 1

The phase shift is pi/6.

 

By phase, we mean the entire quantity inside the trigonometric function, in this case (2/3)x-pi/6. The phase shift is the value of the phase at x=0. You get -pi/6, where the minus sign indicates the trigonometric function is shifted pi/6 radians to the right.

Answer 2

amplitude = 2, the coefficient of sines.

period = 3pi, solving (2/3)P = 2pi for P, the period.

phase shift = pi/4 to the right, since (pi/6)/(2/3) = pi/4