In my technical math midtest I’ve been asked to turn a circle at an offset into its “ball coordinate” representation and at first I was confused about what this ball coordinate means

10 minutes left and I figured it’s probably polar coordinates, so I did that (it had a nice cancellation as well)

Some mistakes:

• I need to compress (cos θ - sin θ), and I forgot how the general equation looks like. I do know that cos(A+B) = cos A cos B - sin A sin B (since I had to prove that earlier), so I just had to figure out what B makes cos B = sin B so I can factor it out later. I thought cos 45° = sin 45° = ½, but it’s not after I left the exam room when I realized it’s not ½ but ½√2

• Turns out what the lecturer meant on “ball coordinate” is the equation r = …, not polar coordinates (though it’s close)

So either way I answered that question wrong