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New way to derive sectors of a circle (easy) 
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#1
Mar2114, 10:46 PM

P: 19

So for starters the area of an entire circle has 360,right?
So we can say that: ##1∏r^2## is ##\equiv## to ##360## So by that logic ##0.5∏r^2## is ##\equiv## to ##180## And finally ##0.25∏r^2## is ##\equiv## to ##90## Divide both sides by 9, and you get : ##0.25∏r^2/9## is ##\equiv## to ##10## From that it's much simpler to multiply both sides by some variable. Simple right? 


#2
Mar2114, 11:31 PM

Sci Advisor
P: 834

How is that any different to the formula on Wikipedia?



#3
Mar2214, 12:17 AM

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P: 21,293




#4
Mar2214, 12:57 AM

HW Helper
P: 3,540

New way to derive sectors of a circle (easy)
Try using \pi in your latex code to produce ##\pi## instead of using the product symbol.
If you want to find the area of a sector of a circle that has angle ##\theta## then multiply the area of a circle by ##\theta/2\pi## so [tex]A=\pi r^2\frac{\theta}{2\pi}=\frac{r^2\theta}{2}[/tex] However, this assumes that the angle is in radians, but if you want to use degrees instead then just use the conversion [tex]\text{angle in radians}=\text{angle in degrees}\times \frac{\pi}{180^o}[/tex] So the formula is then [tex]A=\pi r^2\cdot\frac{\phi}{360}[/tex] Where ##\phi## is in degrees. So if ##\phi=360## which would be the entire circle, then as expected, you get ##A=\pi r^2## 


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