To convert between degrees and radians, you can use the following relationships:
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To convert degrees to radians, use the formula: \[ \text{radians} = \text{degrees} \times \frac{\pi}{180} \]
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To convert radians to degrees, use the formula: \[ \text{degrees} = \text{radians} \times \frac{180}{\pi} \]
Converting Degrees to Radians
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For \(150^\circ\): \[ 150^\circ \times \frac{\pi}{180} = \frac{150\pi}{180} = \frac{5\pi}{6} \]
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For \(40^\circ\): \[ 40^\circ \times \frac{\pi}{180} = \frac{40\pi}{180} = \frac{2\pi}{9} \]
Converting Radians to Degrees
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For \(\frac{5\pi}{4}\): \[ \frac{5\pi}{4} \times \frac{180}{\pi} = \frac{5 \times 180}{4} = \frac{900}{4} = 225^\circ \]
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For \(\frac{\pi}{5}\): \[ \frac{\pi}{5} \times \frac{180}{\pi} = \frac{180}{5} = 36^\circ \]
Summary of Results
- \(150^\circ = \frac{5\pi}{6}\)
- \(40^\circ = \frac{2\pi}{9}\)
- \(\frac{5\pi}{4} = 225^\circ\)
- \(\frac{\pi}{5} = 36^\circ\)