What's the point of Trigonometry?

Some things to try...

• y_s is 200 for all points - this gives amplitude of the motion. Try changing this to 300 - notice that the points go to the very top of the applet.
• ω_y (wy) is 1 - this dictates the speed of the motion change this to 3 to speed it up a bit.
• δ_y (dy) controls the phase. We can put the points out of phase - try the following values:
  • i
  • 18*i
  • -18*i
  • 180*i
  • 185*i

Some things to try...

• If a nineth parameter is equal to 1 then a straight line is drawn instead of a circle. Put ,1 after dy

Lissajous

Lissajous figures are formed when sinusoidal motion is applied to both the x and the y axis.

Some things to try...

• Try changing the phase factors 2 and 5
• Look for a relation between these numbers and the pattern, you can freeze the animation.

Cube

We can generate (x,y,z) points for a cube by taking the triple Cartesian product of n. The sin and cos in the inner SQL tilt this cube. We flatten these into 2D and make the phase correspond to the angle each point makes with the xz plane.

Some things to try...

• Change the angle of tilt (currently .2)
• Add more points to the cube.