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