We need to set up a table of values to see what is happening. We give each point a "point number" so it is easier to understand when we graph the curve.

`t` `0` `π/4` `π/2` `(3π)/4` `π` `(5π)/4` `(3π)/2` `(7π)/4` `2π`
`x` `2` `1.4` `0` `-1.4` `-2` `-1.4` `0` `1.4` `2`
`y` `-0.6` `0.1` `0.7` `1.0` `0.7` `-0.1` `-0.8` `-1.0` `-0.7`
Pt
no.
1 2 3 4 5 6 7 8 9

Here is the resulting curve, with the numbered points included. Point 1 is actually equivalent to Point 9, since we have done one complete cycle of the ellipse as t goes from 0 to 2π.

12-1-21-1xy12345678Open image in a new page

Lissajous figure: Ellipse
x = 2 cos(t),
y = cos(t + 4)

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