ACT Math: Convert Between Degrees and Radians Confidently

180 degrees = π radians. Use this relationship to convert either direction. To convert degrees to radians: multiply by π/180. Example: 90°=(90)(π/180)=π/2 radians. To convert radians to degrees: multiply by 180/π. Example: π/3 radians=(π/3)(180/π)=60 degrees. This one relationship unlocks all angle conversions; memorize it and conversions become mechanical.

Shortcut for common angles: 30°=π/6, 45°=π/4, 60°=π/3, 90°=π/2, 180°=π, 360°=2π. Memorizing these six pairs speeds up problems that use standard angles. But if you forget, use the conversion formula and you still get the right answer.

Error 1: Forgetting to cancel π when converting. Example: 180°=(180)(π/180)=π radians, not 180π radians. The π's cancel. Error 2: Using the wrong multiplier. To go degrees → radians, multiply by π/180, not 180/π. Error 3: Not simplifying the fraction. 45°=(45)(π/180)=45π/180=π/4 (after simplifying by dividing by 45). After each conversion, check: Does my answer look reasonable? Is 90° close to π/2? Yes. Is 180° close to π? Yes.

This sanity check catches most errors immediately.

Convert to radians: (1) 30°, (2) 120°, (3) 270°. Convert to degrees: (4) 5π/6 radians, (5) 3π/2 radians. For each, show your formula and simplification. Answers: (1) π/6, (2) 2π/3, (3) 3π/2, (4) 150°, (5) 270°.

If you missed any, redo them using the formula. By the third attempt, conversions should feel automatic.

Trigonometry and advanced math questions often mix degrees and radians. Being fluent in converting between them saves time and prevents confusion. Master this conversion and you'll solve trigonometry problems 30% faster because you won't stumble on angle units.

Spend 10 minutes memorizing 180°=π radians and the six common angle pairs. Practice the conversions on one problem set. By test day, you'll convert instantly.