On 6/8/18 5:11 PM, Adam Bartoš wrote:

On Fri, Jun 08, 2018 at 10:53:34AM +0200, Adam Bartoš wrote:

Wouldn't sin(45 * DEG) where DEG = 2 * math.pi / 360 be better that sind(45)? This way we woudn't have to introduce new functions. (The

Steven D'Aprano wrote: problem

with nonexact results for nice angles is a separate issue.)

But that's not a separate issue, that's precisely one of the motives for having dedicated trig functions for degrees.

sind(45) (or dsin(45), as I would prefer) could (in principle) return the closest possible float to sqrt(2)/2, which sin(45*DEG) does not do:

py> DEG = 2 * math.pi / 360 py> math.sin(45*DEG) == math.sqrt(2)/2 False

Likewise, we'd expect cosd(90) to return zero, not something not-quite zero:

py> math.cos(90*DEG) 6.123031769111886e-17

That's how it works in Julia:

julia> sind(45) == sqrt(2)/2 true

julia> cosd(90) 0.0

and I'd expect no less here. If we can't do that, there probably wouldn't be much point in the exercise.

But if there are both sin and dsin, and you ask about the difference between them, the obvious answer would be that one takes radians and the other takes degrees. The point that the degrees version is additionally exact on special values is an extra benefit. It would be nice to also fix the original sin, or more precisely to provide a way to give it a fractional multiple of pi. How about a special class PiMultiple that would represent a fractional multiple of pi?

PI = PiMultiple(1) assert PI / 2 == PiMultiple(1, 2) assert cos(PI / 2) == 0 DEG = 2 * PI / 360 assert sin(45 * DEG) == sqrt(2) / 2

Best regards, Adam Bartoš

In one sense that is why I suggest a Circle based version of the trig functions. In effect that is a multiple of Tau (= 2*pi) routine. Richard Damon