And also sec, cosec, cot. But notice they are at least not polynomial in cos and sin, whereas the functions introduced in this article are. To be erudite abou

And also sec, cosec, cot. But notice they are at least not polynomial in cos and sin, whereas the functions introduced in this article are. To be erudite about it, there are essentially no other trig functions than cos and sin, in the sense that cos and sin (aka x and y) generate the ring of polynomial functions on the circle, ℂ[x,y]/(x²+y²-1). Versine etc. are elements of the ring and therefore they are generated (as polynomials) by cos and sin, whereas tan etc. are not elements of the ring because they sometimes go to infinity (they're elements of the larger function field).