Re: [PATCH guile-lib] src: (math trigonometry): Add it.
Maxime Devos <[email protected]> Sun, 16 Feb 2025 12:19:59 +0100
| Newsgroups | gmane.lisp.guile.devel |
|---|---|
| Message-ID | <[email protected]> |
> I'm going to look into what's the case for 'tan'. For 'tan', > tan(pi/4)=tan(45°) is rational as well - I'm going to look into > whether the 'S' of 'tan' is only the integer multiples pi/4, or > whether there are more. > It's only those: For which θ is θ/π and tan(θ) rational? Assume t=tan(θ)∈ℚ. Note that sin (2θ)=(2t)/(1+t^2)∈ℚ. Since sin(2θ) is rational and 2θ/π is rational, then 2θ is an integer multiple of π/2. So, θ is an integer multiple of π/4. (For the other direction, this can be verified with a lookup table.) Best regards, Maxime Devos