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Advanced Mathematics 2200
Trigonometry
2. NL.SO.2200T2
2.4 Converting between degrees and radians
Converting Between Degrees and Radians
A clear, step-by-step guide to converting degrees to radians and radians to degrees, with formulas, examples, and a conversion chart.
What You'll Learn
Degrees and radians are two different units for measuring the same angle, just like inches and centimeters measure the same length.
To convert degrees to radians, multiply by \(\frac{\pi}{180}\); to convert radians to degrees, multiply by \(\frac{180}{\pi}\).
A full circle is 360 degrees, which is the same as \(2\pi\) radians.
Radians are based on the radius of a circle, which is why they are the natural unit for calculus and many trigonometric formulas.
Memorizing a few common conversions, such as 90 degrees equals \(\frac{\pi}{2}\) radians, speeds up later work with the unit circle.
What You'll Practice
1
Converting common angles like 30°, 45°, 60°, and 90° to radians
2
Transforming radian measures back to degrees using π/180 conversion
3
Working with negative angles in both degree and radian forms
4
Simplifying conversions by factoring common terms
Why This Matters
Converting between degrees and radians is essential for advanced math courses like calculus and physics. Radians are the standard unit in higher mathematics, and mastering these conversions helps you work with trigonometric functions, graphs, and unit circles efficiently.
Before You Start — Make Sure You Can:
This Unit Includes
3 Video lessons
Learning resources
Skills
Radians
Degrees
Unit Conversion
Pi
Trigonometry
Special Triangles
Angle Measurement
NL Curriculum Aligned