y cos 3x pi 2 Determine the amplitude range period phase sh

y= -cos (3x + pi) -2

Determine the amplitude, range, period, phase shift, and give the quarter points

Solution

y= -cos (3x + pi) -2

comparing it with standard cosine function : y = Acos(BX +C) +D

where Amplitude = A ;T= 2pi/B ; phase shift = C/B

Amplitude A = 1

period T = 2pi/3

phase shift = pi/3

Range : -2+1 and -2 -1 ---> [ -3 , -1 ]

Quarter points : Start with x =0 : y = -1

Now divide one period in 4 parts: 2pi/3*4 = pi/6

So, x = pi/6 ; y = =-cos( pi/6+pi) -2 = -1.13

x = pi/3 ; y = - cos(pi +pi/3) -2 = -1.5

x = pi/2 ; y = -cos(pi/2 +pi/3) -2 = -2

x = 2pi/3 ; y = -cos( 2pi/3 +pi/3) -2 = -1