How special is 1, in radians of course.

What's the significance of \(\cos(1)?\) \(\sin^{-1}(1)\).

I've been wondering about these questions for the past few days. I even tried to derive \(\sin(1)\) by calculus without a calculator, and I managed to get to \(1=\sin^{-1}(1)+\sin^{-1}(p)\) where p is \(\cos(1)\), but you of course need a calculator from here.

So is there any significance to \(\cos(1)\) and how would you derive it? (Without using a calc)

It also just crossed my mind, but what's significant about 1 radian in degrees?

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## Comments

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TopNewestYou can derive sin(1) by using taylor series of sin function to any disired accuracy. Ofcourse sin(1) is transcendental hence it has no closed form in terms to square roots or n-th roots, and any finite sequence of basic operation on integers.

Hence I would like to conclude that there is nothing too significant for something like sin(1).

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You can use linear approximation using derivative since a radian is very close to sixty degrees.

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