Some curious Property of sin(x) for values near zero measured in degrees.

We have some wild approximation, sin(1) is approximately π/180 when measured in degrees. sin(1/2) is approximately π/360. sin(1/180) is approximately π/32400. Now the pattern you see is simply sin(1/x)=π/(180x) for x being an integer greater than or equal to 1. Again as another property for large x , 180xsin(1/x)=π when measured in degrees. Another one is tan(1/x) is approximately sin(1/x) for x being an integer greater than or equal to 1.Hence concluding , Area of a circle = 180x sin(1/x) times radius squared for x being greater than or equal to 1 and when measured in degrees.

#Geometry

Easy Math Editor

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Comments

Relevant article: Maclaurin series.

Pi Han Goh - 1 year ago

It is true that we can use the Maclaurin series to prove it but the problem for me was that I didn't knew anything about infinite series when I proved it.You see I proved it in a more Pythagorean way and I would like to send my own proof.

Aruna Yumlembam - 1 year ago

Math	Appears as
Remember to wrap math in `\(` ... `\)` or `\[` ... `\]` to ensure proper formatting.
`2 \times 3`	$2 \times 3$
`2^{34}`	$2^{34}$
`a_{i-1}`	$a_{i-1}$
`\frac{2}{3}`	$\frac{2}{3}$
`\sqrt{2}`	$\sqrt{2}$
`\sum_{i=1}^3`	$\sum_{i=1}^3$
`\sin \theta`	$\sin \theta$
`\boxed{123}`	$\boxed{123}$