Converting Between Degrees and Radians

Trigonometry · Axiom Academy

EXAMPLE Converting Between Degrees and Radians Master the conversion process with two complete examples: degrees to radians and radians to degrees. Part 1: Converting 150° to Radians Part 2: Converting 5π/6 Radians to Degrees Excellent work! You've mastered converting between degrees and radians. Here's what to remember: Degrees to Radians: Multiply by π/180° to convert. The degree units cancel, leaving radians. Radians to Degrees: Multiply by 180°/π to convert. The π cancels, leaving degrees. Simplify Fractions: Always reduce your answer to lowest terms by finding the GCD of numerator and denominator. Unit Cancellation: The conversion factors are designed so units cancel properly—this helps verify you're using the right formula! Common Angles: Memorizing conversions for multiples of 30° and 45° (like 30°=π/6, 45°=π/4, 60°=π/3) speeds up work significantly. These conversions are fundamental in trigonometry—you'll use them constantly when working with trig functions, unit circles, and periodic motion. Practice until the process becomes automatic!

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