Degree and radian measure
Degree and radian measure in the unit circle.
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Study Degree and radian measure
Angle measurement: radian
Starting point: unit circle in the plane
The length of the complete arc = equals the circumference of a circle with radius \(1\) and hence is equal to \(2\pi\).
angle \(\alpha\) = length of the arc between \((1,0)\) and \((b,a)\)
Conversion from degree to radian
We have: \[\frac{\text{degrees}}{360{^\circ}}=\frac{\text{radians}}{2\pi}\]
Let \(\alpha\) be an angle which has as degree the form \(x{^\circ}\). Then radian can be calculated as follows: \[{}\alpha=\frac{{x}}{180}\cdot\pi.\]
Example 1.
| degrees | \(0^{\circ}\) | \(30^{\circ}\) | \(45^{\circ}\) | \(60^{\circ}\) | \(90^{\circ}\) | \(180^{\circ}\) | \(270^{\circ}\) | \(360^{\circ}\) |
|---|---|---|---|---|---|---|---|---|
| radians | 0 | \(\frac{\pi}{6}\) | \(\frac{\pi}{4}\) | \(\frac{\pi}{3}\) | \(\frac{\pi}{2}\) | \(\pi\) | \(\frac{3\pi}{2}\) | \(2\pi\) |
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