Register to reply

New way to derive sectors of a circle (easy)

by shadowboy13
Tags: circle, derive, sectors
Share this thread:
shadowboy13
#1
Mar21-14, 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?
Phys.Org News Partner Mathematics news on Phys.org
'Moral victories' might spare you from losing again
Fair cake cutting gets its own algorithm
Effort to model Facebook yields key to famous math problem (and a prize)
pwsnafu
#2
Mar21-14, 11:31 PM
Sci Advisor
P: 820
How is that any different to the formula on Wikipedia?
Mark44
#3
Mar22-14, 12:17 AM
Mentor
P: 21,216
Quote Quote by shadowboy13 View Post
So for starters the area of an entire circle has 360,right?
For starters, the area of a circle is not 360. That's the measure of the angle of a sector.
Quote Quote by shadowboy13 View Post

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?

Mentallic
#4
Mar22-14, 12:57 AM
HW Helper
P: 3,510
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##


Register to reply

Related Discussions
Derive the general formula of the equation of a circle for the points Precalculus Mathematics Homework 11
Fill with color three of five sectors in circle with latex. Math & Science Software 0
Seemingly easy circle geometry... can't figure it out. General Math 9
Circle easy question, Precalculus Mathematics Homework 3
Hidden sectors High Energy, Nuclear, Particle Physics 2