# Rotating a Function

You can pretty easily use parametric equations to rotate a function through any angle of rotation.

1.  Define a function, f(x)
2. Either choose an angle measure, a, or leave a as a slider and type in this parametric equation: (t·cos f(t)·sin a, t·sin a+f(t)·cos a)
3. You’ll need to specify the values of t.  I generally use -20 to 20, because that will cover what is visible in a normal zoom.  If you want to zoom out quite a bit, though, you may want larger values as your bounds on t.
4. If you want to animate the rotation, specify the bounds on the slider a.

Check out this example!  Click on the image of the graph and it will take you to the full, rotating version on Desmos!

Note, that you can press play on the slider.  While it’s playing, you can adjust the speed and whether or not the slider cycles through in one direction or goes back and forth.

vs.

if you want to make a continuously rotating graph, adjust the bounds on your slider, a, to 0 to 6.28 (if you’re in radian mode) and then after you press play, click the two cycling arrows you see to the left.  This will allow you to toggle between the types   If you just want to adjust the speed, click the forward and backward symbols: « and ».

Check out this graph I made (purely for the fun of it) using the idea of rotations!

I had to figure out how to get the clock hands to rotate clockwise, because with my original parametric equations, they were rotating counter clockwise.  So after some playing around, I realized that I could use this set of parametric equations instead: (-t·cos a +f(t)·sin a, t·sin a+f(t)·cos a) and voila!  Problem solved!