Determine the amplitude period and phase shift for the given

Determine the amplitude, period, and phase shift for the given function. y = sin (2x - pi/6) amplitude 1 period pi phase shift Graph the function over one period. Indicate the x-intercepts of the graph. (x, y) = () (smallest x-value) (x, y) = () (x, y) = () (largest x-value) Indicate the coordinates of the highest point on the graph. (x, y) = (pi/3, 1) Indicate the coordinates of the lowest point on the graph. (x, y) = (5 pi/6, -1)

Solution

y = sin(2x-/6)

Phase shift = /12 to the right

X-intercept :

When y = 0 , => Sin(2x-/6)= 0 = sin0 = sin= sin2

x= /12 , x=7/12 , x= 13/12

(/12 , 0) - smallest x value

(7/12,0)

(13/12,0) largest x value