We draw a table of values:

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

The sketch is:

12-1-21-1xy1 = 7 = 92 = 63 = 548Open image in a new page

Lissajous figure: Parabola (part)
x = cos(t + π/4),
y = sin(2t)

This curve is part of a parabola.

Of course, it would have been better to start our values from `t = (3π)/4` (Point 4) and only use Points 4, 5, 6, 7, and 8, but often you don't know that until you have drawn it.

Easy to understand math videos:
MathTutorDVD.com