Sector of an Ellipse
Ellipse sector (a two-dimensional figure) is a part of the interior of an ellipse having two radius boundries and an arc.- Sector is a fraction of the area of a ellipse with a radius on each side and an edge.
- Major axis is always the longest axis in an ellipse.
- Minor axis is always the shortest axis in an ellipse.
- Semi-major axis is half of the longest axis of an ellipse.
- Semi-minor axis is half of the shortest axis of an ellipse.
Sector Area formula |
||
| \(\large{ A_{area} = \frac{a\;b}{2} \; \left( {\theta \;-\; atan\;\left[ \frac{ a\;-\;b \;sin\;\left(2\;\theta_1\right) }{ a\;+\;b\;+\;\left(a\;-\;b\right)\;cos\left(2\;\theta_2\right) } \right] \;+\; atan\;\left[ \frac{ a\;-\;b \;sin\;\left(2\;\theta_1\right) }{ a\;+\;b\;+\;\left(a\;-\;b\right)\;cos\;\left(2\;\theta_2\right) } \right] } \right) }\) | ||
| Symbol | English | Metric |
| \(\large{ A_{area} }\) = area | \(\large{ in^2 }\) | \(\large{ mm^2 }\) |
| \(\large{ \theta }\) = angle | \(\large{ deg }\) | \(\large{ rad }\) |
| \(\large{ \theta_1 }\) = angle | \(\large{ deg }\) | \(\large{ rad }\) |
| \(\large{ \theta_2 }\) = angle | \(\large{ deg }\) | \(\large{ rad }\) |
| \(\large{ a }\) = semi-major axis | \(\large{ in }\) | \(\large{ mm }\) |
| \(\large{ b }\) = semi-minor axis | \(\large{ in }\) | \(\large{ mm }\) |
Sector Radius formula |
||
|
\(\large{ j = \sqrt{ \frac{a^2\;b^2}{a^2\;sin^2 \;\theta_1 \;+\; b^2\;cos^2 \;\theta_2} } }\) \(\large{ k = \sqrt{ \frac{a^2\;b^2}{a^2\;sin^2 \; \theta_2 \;+\; b^2\;cos^2\;\theta_1} } }\) |
||
| Symbol | English | Metric |
| \(\large{ j }\) = radius | \(\large{ in }\) | \(\large{ mm }\) |
| \(\large{ k }\) = radius | \(\large{ in }\) | \(\large{ mm }\) |
| \(\large{ \theta_1 }\) = angle | \(\large{ deg }\) | \(\large{ rad }\) |
| \(\large{ \theta_2 }\) = angle | \(\large{ deg }\) | \(\large{ rad }\) |
| \(\large{ a }\) = semi-major axis | \(\large{ in }\) | \(\large{ mm }\) |
| \(\large{ b }\) = semi-minor axis | \(\large{ in }\) | \(\large{ mm }\) |
