const PI = atan(1) * 4Note that despite involving code, I"m asking this from a khansar.netematics perspective.

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Is this an estimation of PI, or should it give me a large degree of accuracy?How does this give PI?

On the second point, if I understand atan correctly, it takes a ratio of two sides, and returns the corresponding angle.

That means that atan(1) is referring a situation with 2 equal length sides.

I think I"m misunderstanding something though, as atan(1) gives me 0.7853981633974483, which seems like a very tiny angle.

If anyone can fill in the holes, it would be greatly appreciated.

pi
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asked Mar 29, 2015 at 17:26 CarcigenicateCarcigenicate
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I"m including this little gif from Wikipedia as a great way to lớn understand radians. nói qua
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answered Mar 29, năm ngoái at 17:47 JoffanJoffan
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The function \$arctancolon khansar.netbbR o (-fracpi2,fracpi2)\$ is the inverse of \$ an\$. (for the right domain name of definition). As \$ an fracpi4 = 1\$, this means that \$arctan 1=fracpi4\$.

Regarding your question about angles: angles are (in khansar.netematics) measured in radians (in \$<0,2pi)\$ or \$<-pi,pi)\$), not in degrees: you should expect a value or order \$pi\$ or so, not ranging between \$0\$ and \$360\$.

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edited Mar 29, 2015 at 18:01
answered Mar 29, năm ngoái at 17:29 Clement C.Clement C.
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You certainly know that \$sinfracpi4=cosfracpi4=fracsqrt22\$ so one has \$ anfracpi4=1\$ & therefore \$pi=4 an^-11\$

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answered Mar 29, 2015 at 17:32 marwalixmarwalix
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khansar.net explanation from a non-khansar.net person:

In a right angled triangle if the two short sides are equal, the angle is 45 degrees.

45 degrees in radians is π/4. (The full circumference is 2πr, 180 degrees is π & 45 degrees is π/4)

sin π/4 = cos π/4 because the two sides are equal.

tan π/4 = rã 45 = 1.

Arctan(1) is the degree (or radian) which returns a value of 1. So arctan of 1 is either 45 degrees or π/4.

π = 4*arctan(1)

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answered Jun 19, 2018 at 19:24 gizmogizmo
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This shows geometric explanation for relationship between tan, atan & Pi.

Because horizontal segment AB = 1 & vertical segment BD = 1, angle alpha = 45°. From there you can use atan( BD ) lớn determine 45° in radiant and take that times 4 to lớn get Pi. tóm tắt
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answered Sep 17, 2020 at 9:30
VisorZVisorZ
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You are correct, in all numeric programing languages lượt thích fortran, c, c++, & many others, for a program generalized input đầu vào line that looks something like:

print, numeric, %pi , acos(-1), 4*atan(1)all return the same numeric value. Here the system stored value %pi may be faster than trig evaluation.

3.141592653589793, 3.141592653589793, 3.141592653589793
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answered Mar 4, 2018 at 20:44
eromanaeromana
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Thanks for contributing an answer to lớn khansar.netematics Stack Exchange!

But avoid

Asking for help, clarification, or responding khổng lồ other answers.Making statements based on opinion; back them up with references or personal experience.

Use khansar.netJax khổng lồ format equations. khansar.netJax reference.

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