How would you graph a wave function going through specific points.

Question

I am a programmer and a project I am working on requires me to rotate an object around an axis. The default axis for my canvas is (0, 0) (the canvas is a 400 by 400 square). I need to rotate an object at an axis point of (200, 200) using translation's. Note that I am rotating using degree's. I only currently have the translation for 9 point's of rotation which are: 45° 90° 135° 180° 225° 270° 315° 360° all which are standard degree point's.

These are the translation's it have now: for 45°(200, -82.843); 90°(400, 0); 135°(482.843, 200); 180°(400, 400); 225°(200, 482.843); 270°(0, 400); 315°(-82.842, 200); 360°(0, 0);.I graph each point seperatly, such as if I wanted to graph the translation for 45° I would make two graphs, one for x and one for y of the translation, like this:(45, 200) and (45, -82.843). The translation's make a sort of wave function. I haven't found any online calculator's capable of turning a table into a graph. It would be great to get an equation for these point's. Thank you :)

*There should be two equation's, one for the translation's x where the points would look like this (degree, translation X) and for y: (degree, translation Y)

Answer 1

If the point of rotation is (0, 0), then y = r sin θ and x = r cos θ, where r = radius.

Assuming the radius is 200,

y = 200 cos θ, x = 200 sin θ.

For 0°

y = sin 0°, x = cos 0°

y = 0, x = 200

For 45°

y = 200 cos 45°, x = 200 sin 45°

y = 200(√2/2), x = 200 (√2/2)

Does this do it?