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
