1 cycle = 1 "tau" radians. It's important to include units. I don't see how keeping irrational "magic numbers" out of the equation could make it anything but simpler. As an added benefit, it would serve as a transition between degrees and radians, by introducing the idea that there are multiple measures for an angle without simultaneously introducing a unit that has irrational values in every useful situation.
I agree that degrees are terrible, but sin(1/4)=1 makes a lot of sense. Probably even more than sin(1/4 tau)=1. The only reason to use radians instead of cycles is that changing the units breaks the wonderful trig derivative symmetry.
Radians are pure numbers (which is why I left them out). That said, I see what you mean now and I agree. sin(1/4 of a circle) makes more sense than sin(1/4 tau) which makes more sense than sin(1/4 360).
Comments
1 cycle = 1 "tau" radians. It's important to include units. I don't see how keeping irrational "magic numbers" out of the equation could make it anything but simpler. As an added benefit, it would serve as a transition between degrees and radians, by introducing the idea that there are multiple measures for an angle without simultaneously introducing a unit that has irrational values in every useful situation.
I agree that degrees are terrible, but sin(1/4)=1 makes a lot of sense. Probably even more than sin(1/4 tau)=1. The only reason to use radians instead of cycles is that changing the units breaks the wonderful trig derivative symmetry.
Radians are pure numbers (which is why I left them out). That said, I see what you mean now and I agree. sin(1/4 of a circle) makes more sense than sin(1/4 tau) which makes more sense than sin(1/4 360).
Danger being, of course, that sin(1/4) != 1.
(sin(0.25) = 0.247403959)
If your sin function is calibrated to take radians, then yes. If it's calibrated to take cycles, sin(1/4) = 1.
Ahh yes, of course. My apologies!