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[h] SL 3.4 The circle radian measure of angles
[q] Radians
[a] Ever since elementary school, you have measured angles in degree with 360° representing a “full-tun”, 90° represnting a right- angle, etc.
Now, we learn an alternative to degrees which is radian. Radians are measured with:
2π = 360° , π radians = 180° , \(\frac{π}{2} radians = 30°\), etc.
You can convert with: \(\frac{degrees}{180}×π = radians \) and \(\frac{radian}{π}× 180° = degrees\).
Usage of radians is more vital in trigonometry, calculus, etc. Unless you see degrees specially mentioned in the question then, you should use radians.
[q] Sector
[a] The fraction of the area of circle is called a “sector”.
[q] Arc
[a] The fraction of the circumference of cirle is called an “arc”.
[q] Arc Length
[a] As a full circumference is found with \(C=2πr\) and we are considering \(\frac{\theta}{360°}\) or \(\frac{\theta}{2π}\) of the circumference then, arc length = \(2πr× \frac{\theta}{2π}= \theta×r\).
[q] Sector Area
[a] As a full circle area is found with \(A=πr^2\) and we are considering \(\frac{\theta}{2πr^2}\) of the circumference then, sector area = \(πr^2× \frac{\theta}{2π}= \theta×r = \frac{1}{2}×\theta×r^2\).
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