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| Definition of One Radian |
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The angle subtended at the centre of a circle is \(1\) radian if the length of the arc is equal to the radius of the circle.
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| Relationship with Degrees |
- \(1\text{ rad}=\dfrac{180^\circ}{\pi}\)
- \(360^\circ=2\pi \text{ rad}\)
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| Conversion Formula |
- To convert degrees to radians:
\(\text{radians}=\text{degrees}\times \dfrac{\pi}{180^\circ}\)
- To convert radians to degrees:
\(\text{degrees}=\text{radians}\times\dfrac{180^\circ}{\pi}\)
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| Example \(1\) |
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Convert \(120^\circ\) to radians.
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\(\begin{aligned} \text{radians}&=120^\circ\times\dfrac{\pi}{180^\circ} \\\\ &=\dfrac{2\pi}{3}\text{ rad} .\end{aligned}\)
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| Example \(2\) |
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Convert \(\dfrac{\pi}{4}\text{ rad}\) to degrees.
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\(\begin{aligned} \text{degrees}&=\dfrac{\pi}{4}\text{ rad}\times\dfrac{180^\circ}{\pi} \\\\ &=45^\circ. \end{aligned}\)
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