Counterclockwise or clockwise rotation checks out correctly. Slowing the clock speed lets you check the direction of rotation. 1 - 179 degree of phase angle gives counterclockwise rotation. 181 -359 degrees of phase angle gives clockwise rotation. 0 and 180 degrees of phase angle gives sloped lines.
DESMOS Graphing app gives a vertical and horizontal sine wave for these equations and not a Lissajous image. You have to XY display the two sine waves to get the Lissajous curve displayed.
0 phase angle:
x(t)=sin(2 X pi x t)
y(t)=sin(2 X pi X t - 0)
45 phase angle:
x(t)=sin(2 X pi x t)
y(t)=sin(2 X pi X t -( pi/4))
90 phase angle:
x(t)=sin(2 X pi x t)
y(t)=sin(2 X pi X t -( pi/2))
135 phase angle:
x(t)=sin(2 X pi x t)
y(t)=sin(2 X pi X t -(3 pi/4))
180 phase angle:
x(t)=sin(2 X pi x t)
y(t)=sin(2 X pi X t - pi)
225 phase angle:
x(t)=sin(2 X pi x t)
y(t)=sin(2 X pi X t -( 5pi/4))
270 phase angle:
x(t)=sin(2 X pi x t)
y(t)=sin(2 X pi X t -( 3pi/2))
315 phase angle:
x(t)=sin(2 X pi x t)
y(t)=sin(2 X pi X t -(7pi/4))
