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Degrees to Radians

Part of the Angles and the Unit Circle section of Coddy's Trigonometry journey. Lesson 13 of 55.

π\pi radians and 180° are the same half turn. Divide both by 180: one degree is π180\frac{\pi}{180} radians. So multiply an angle in degrees by π180\frac{\pi}{180} to get radians.

Take 150°: 150⋅π180\frac{150\cdot \pi}{180}. 150 and 180 share a factor of 30, so the fraction reduces to 5/6 and 150° is 5π6\frac{5\pi}{6} radians.

Leave radian answers as a fraction of π\pi. That keeps them exact and shows the size at a glance: 5π6\frac{5\pi}{6} is five sixths of a half turn, just short of π\pi.

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Challenge

Turn 210° into radians. On the blank board, write x as the conversion, then a line with x exact, as a fraction of π\pi in lowest terms. Then press Check.

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This lesson includes a short quiz. Start the lesson to answer it and track your progress.

quiz iconTest yourself

This lesson includes a short quiz. Start the lesson to answer it and track your progress.

All lessons in Angles and the Unit Circle