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 of an Ellipse Index
Area Sector of an Ellipse formula |
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| \( A_{area} \;=\; \frac{a\;b}{2} \; \left( {\theta \;-\; atan\left[ \frac{ a\;-\;b \;sin(2\;\theta_1) }{ a\;+\;b\;+\;\left(a\;-\;b\right)\;cos(2\;\theta_2) } \right] \;+\; atan\left[ \frac{ a\;-\;b \;sin(2\;\theta_1) }{ a\;+\;b\;+\;\left(a\;-\;b\right)\;cos(2\;\theta_2) } \right] } \right) \) | ||
| Symbol | English | Metric |
| \( A_{area} \) = area | \( in^2 \) | \( mm^2 \) |
| \( \theta \) = angle | \( deg\) | \( rad \) |
| \( \theta_1 \) = angle | \( deg \) | \( rad \) |
| \( \theta_2 \) = angle | \( deg \) | \( rad \) |
| \( a \) = semi-major axis | \( in \) | \( mm \) |
| \( b \) = semi-minor axis | \( in \) | \( mm \) |
Radius Sector of an Ellipse formula |
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\( j \;=\; \sqrt{ a^2\;b^2 \;/\; a^2\;sin^2 (\theta_1) + b^2\;cos^2 (\theta_2 ) } \) \( k \;=\; \sqrt{ a^2\;b^2 \;/\; a^2\;sin^2 (\theta_2) + b^2\;cos^2 (\theta_1) } \) |
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| Symbol | English | Metric |
| \( j \) = radius | \( in \) | \( mm \) |
| \( k \) = radius | \( in \) | \( mm \) |
| \( \theta_1 \) = angle | \( deg \) | \( rad \) |
| \( \theta_2 \) = angle | \( deg \) | \( rad \) |
| \( a \) = semi-major axis | \( in \) | \( mm \) |
| \( b \) = semi-minor axis | \( in \) | \( mm \) |
Tags: Ellipse