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New way to derive sectors of a circle (easy)

  1. Mar 21, 2014 #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. Mar 21, 2014 #2

    pwsnafu

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    Science Advisor

    How is that any different to the formula on Wikipedia?
     
  4. Mar 22, 2014 #3

    Mark44

    Staff: Mentor

    For starters, the area of a circle is not 360°. That's the measure of the angle of a sector.
     
  5. Mar 22, 2014 #4

    Mentallic

    User Avatar
    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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