The original Asteroids source code has been released, we can look at what it did! (Also, even before that the EPROM images had been disassembled, but looking at the original sources is more fun.)

It indeed used (-128, 128) for (-180°,180°)

For instance, here it is using 64 (written as "40", because hexadecimal) for "PI/2":

    COS:    CLC                     ;COS(A)=SIN(A+PI/2)
            ADC I,40
    ;       JMP SIN

It implements COS in terms of SIN, and SIN wraps everything to be in the domain [0,64] (that is [0°,90°] ) then retrieves that from the lookup table.

code: https://github.com/historicalsource/asteroids/blob/main/A351...

table: https://github.com/historicalsource/asteroids/blob/main/A351...

Pico8 is 128x18 res, so I think the maximum number of visibly unique lines you could draw from one point is 512. You can't even express sub-one-degree (sub-1.422222 really) rotations on Pico8 visually without subsampling etc.

You can always do one cycle of newton-raphson to get nearly double the accuracy with only one extra lookup-multiply-add.

The sin/cos lookup tables would only contain an octant of the circle and use various symmetries to map other values to that range. Thus the resolution is ~0.176 degrees for a 256-entry table.

sin(x) = -sin(-x) = sin(pi - x) = cos(pi/2 - x)

cos(x) = cos(-x) = -cos(pi - x) = sin(pi/2 - x)