# New way to derive sectors of a circle (easy)

1. Mar 21, 2014

So for starters the area of an entire circle has 360º,right?

So we can say that: $1∏r^2$ is $\equiv$ to $360º$

So by that logic $0.5∏r^2$ is $\equiv$ to $180º$

And finally $0.25∏r^2$ is $\equiv$ to $90º$

Divide both sides by 9, and you get : $0.25∏r^2/9$ is $\equiv$ to $10º$

From that it's much simpler to multiply both sides by some variable.

Simple right?

2. Mar 21, 2014

### pwsnafu

How is that any different to the formula on Wikipedia?

3. Mar 22, 2014

### Staff: Mentor

For starters, the area of a circle is not 360°. That's the measure of the angle of a sector.

4. Mar 22, 2014

### Mentallic

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

$$A=\pi r^2\frac{\theta}{2\pi}=\frac{r^2\theta}{2}$$

However, this assumes that the angle is in radians, but if you want to use degrees instead then just use the conversion

$$\text{angle in radians}=\text{angle in degrees}\times \frac{\pi}{180^o}$$

So the formula is then

$$A=\pi r^2\cdot\frac{\phi}{360}$$

Where $\phi$ is in degrees. So if $\phi=360$ which would be the entire circle, then as expected, you get $A=\pi r^2$