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Learn how to convert between degrees and radians, and understand radian measure.
Learn step-by-step with practice exercises built right in.
A radian is the angle formed when the arc length equals the radius of a circle.
Key insight: One complete revolution around a circle is radians (or ).
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Avoid these 4 frequent errors
See how this math is used in the real world
A stone is dropped into a still pond, creating a circular ripple. The radius of the ripple is increasing at a rate of cm/s. How fast is the area of the circle increasing when the radius is cm?
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This is the most important relationship to remember!
Formula: Multiply by
Example 1: Convert to radians
Example 2: Convert to radians
Formula: Multiply by
Example 1: Convert to degrees
Example 2: Convert to degrees
Memorize these frequently used conversions:
| Degrees | Radians | Notes | |---------|---------|-------| | | | Starting point | | | | Half of | | | | Quarter turn | | | | Twice | | | | Right angle | | | | Twice | | | | Three times | | | | Five times | | | | Straight angle | | | | Three-quarter turn | | | | Full circle |
To convert degrees to radians mentally:
Example: