New way to derive sectors of a circle (easy)

  1. 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. jcsd
  3. pwsnafu

    pwsnafu 902
    Science Advisor

    How is that any different to the formula on Wikipedia?
     
  4. Mark44

    Staff: Mentor

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

    Mentallic 3,660
    Homework Helper

    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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