What are the five quarter points for the equations ysin14x y

What are the five quarter points for the equations:

y=sin(-1/4x)

y=2sin(4x)

y=cos (x+3pi/2)

Solution

1) y = sin(-x/4)

period = 2pi/ 1/4 = 8pi

five quarte points : are x= 0 , 8pi/4 , 8pi/2, 8pi/4 +8pi/2 , 8pi

x = 0, 2pi , 4pi , 6pi, 8pi

Find y = sin(-x/4) for these points y = 0 , -1 , 0 , 1 , 0

2) y = 2sin4x

period = 2pi/4 = pi/2

Five quarter points : x= 0, pi/8 , pi/4, 3pi/8 , pi/2

Values of y = 2sin(4x) ; y=0 , 2 , 0, -2 , 0

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

period = 2pi/1 = 2pi

phase shift = 3pi/2

So, five quarter points are : x = 0 +3pi/2 , 2pi/4 +3pi/2 , 2pi/2 +3pi/2 , 2pi/2 +2pi/4 +3pi/2 , 2pi +3pi/2

x = 3pi/2 , 2pi , 5pi/2 , 3pi , 7pi/2

y = cos(3pi) = 0 , 1 , 0 ,-1 , 0

What are the five quarter points for the equations: y=sin(-1/4x) y=2sin(4x) y=cos (x+3pi/2)Solution1) y = sin(-x/4) period = 2pi/ 1/4 = 8pi five quarte points :

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