const PI = atan(1) * 4Note that despite involving code, I"m asking this from a khansar.netematics perspective.
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I have 2 questions about this:
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.
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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.
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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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