/mg/ - Math General

Is there an expression equivalent to arccos((a*cos(x) + f)/(a + f*cos(x))) which does not use an inverse trig function or infinite series? Where a and f are constants and a > f > 0.

My physical intuition tells me "no."

My physical intuition tells me "yes".

What is the physical intuition for the axiom of infinity?

I don't see a proof of this group supposedly being "abelian" in your post.

My physical intuition tells me "maybe".

arccos((a*cos(x) + f)/(a + f*cos(x))) =

π/2 + i log((i (f + 1/2 a (e^(-i x) + e^(i x))))/(a + 1/2 f (e^(-i x) + e^(i x))) + sqrt(1 - (f + 1/2 a (e^(-i x) + e^(i x)))^2/(a + 1/2 f (e^(-i x) + e^(i x)))^2))

What is the last "how to self-learn math" pasta nowadays? I want to brush up calc 1 and Linear algebra and go from there.

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Nice meme.