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

Tags: circle, derive, sectors
 HW Helper P: 3,543 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 $$A=\pi r^2\frac{\theta}{2\pi}=\frac{r^2\theta}{2}$$ 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##