Cobra

class Trig
    const mod as float = 0.0174532925199433f #0.017453292519943295769236907684886127134 = tau/360
    var time as System.Diagnostics.Stopwatch = System.Diagnostics.Stopwatch()
    var output as List<of String> = List<of String>()
    def main
        for line in File.readLines('trig.in'), .output.add(.compute(float.parse(line)) + '\n')
        File.writeAllLines('trig.out', .output)
        print .time.elapsed
    def compute(degrees as float) as String
        .time.start
        if degrees % 180
            rad as float = sin as float = degrees * .mod
            two as float = rad * rad
            sin -= (rad *= two) / 6
            sin += (rad *= two) / 120
            sin -= (rad *= two) / 5040
            sin += (rad *= two) / 362880
            sin -= (rad *= two) / 39916800
            sin += (rad *= two) / 6227020800
            sin -= (rad *= two) / 1307674368000
            sin += (rad *= two) / 355687428096000
            sin -= (rad *= two) / 121645100408832000
            sin += (rad *= two) / 51090942171709440000f
            sin -= (rad *= two) / 25852016738884976640000f
            sin += (rad *= two) / 15511210043330985984000000f
            sin -= (rad *= two) / 10888869450418352160768000000f
            sin += (rad *= two) / 8841761993739701954543616000000f
        else, sin as float = 0
        if degrees % 180 <> 90, cos as float = Math.sqrt(1 - sin * sin) * ((Math.abs(degrees - 180) - 90) / Math.abs(Math.abs(degrees - 180) - 90))
        else, cos as float = 0
        tan as float = sin / cos
        .time.stop
        return sin.toString('0.000000E+0') + ' ' + cos.toString('0.000000E+0') + ' ' + tan.toString('0.000000E+0')

Compile it with cobra filename -turbo

The output is now 100% accurate to the specified number of sigfigs,
and is almost as fast as the inbuilt functions (but more accurate).

Tests: AMD FX6300 @5.1GHz

• The 360 * 10000 test used by the C answer runs in 652ms (vs 190ms)

• The 4-entry test used by the Python answer runs in 4.6µs (vs 50µs)

• The 1000 random angle test used by the Fortran answer runs at 180ns per angle (vs 10µs)