State the amplitude period and phase shift and then sketch o

State the amplitude, period and phase shift, and then sketch one complete cycle of the graph. Label all maximum, minimum and x-intercepts. a) y = 3cos(2x + pi) b) y = 2sin(4x - pi) c) y = -4 sin (x - pi/2)

Solution

a) Comparing it with eqn y = acos(bx +c) + d, we see that

a = 3 Hence amplitude is 3

b = 2 Hence period is 2.pi/b = 2.pi/2 = pi

c = pi Phase shift is -c/b = -pi/2

b) Comparing it with y = asin(bx - c)

Amplitude a = 2

Period = 2pi/b = 2pi/4 = pi/2

Phase shift c/b = pi/4

c) y = -4sin(x-pi/2)

Ampltude is |a| = 4

period = 2pi/1 = 2pi

phase shift c/b = pi/2