lz_sine
The sine of an angle.
long lz_sine( CLZNumber* leftOperand, CLZNumber* targetNumber = nullptr );Correctly rounded. In radians the argument is reduced modulo 2π against a constant carried far enough for the argument's size, so even the sine of 1020 keeps every place. It is then folded into [0, π/4] and summed as a Taylor series, at wide widths by binary splitting.
In degrees, grads or millicles the angle is reduced by whole turns exactly, and an angle whose sine is a rational number is answered exactly: sin 30° is 0.5, and 100 grads is a right angle.
Examples
| Call | Answer |
|---|---|
lz_sine( 1 ) | 0.841470984807896506652502321630299000 |
lz_sine( 30 ) degrees | 0.5 |
lz_sine( 1E20 ) | −0.645251285265780844205811711312523007 |
lz_sine( 100 ) grads | 1 |
Each answer is what Addaptic printed for the call, in radians, at 36 places unless a setting is shown.
Returns
kNoError (0) when the answer is written. Otherwise an error code, with the answer flagged infinite or not-a-number; see Errors and flags.
See also
lz_cosineThe cosine of an angle.lz_sine_cosineThe sine and the cosine of one angle together, for about half the cost of the two.lz_arcsineThe angle whose sine is the number.lzc_sineThe sine of a complex angle.