Mathematics — first biennium · Lesson
A radian measures an angle through the arc-to-radius ratio. On the unit circle 180° correspond to π radians, so θ° = θ/180·π.
Prerequisites: Angles, real numbers and circle geometry
Goal: Convert between degrees and radians and interpret an oriented angle on the unit circle.
In this lesson: Convert between degrees and radians and interpret an oriented angle on the unit circle.
New concept: One radian is the central angle subtending an arc whose length equals the radius. A full turn is 2π radians and 360°, so π rad=180°; this equality is the basis for conversions.
How to proceed: First reduce degrees/180. The answer field contains only the coefficient multiplying π.
You can already assume: Angles, real numbers and circle geometry.
The angle is measured on the unit circle; degrees and radians describe the same rotation.
Completed exercises: 0/5 · Correct on first attempt: 0
First reduce degrees/180. The answer field contains only the coefficient multiplying π.
Data / situation: Convert 30° to radians as a coefficient of π.
ConceptStep separates what is required from what is recommended or useful as reinforcement. Only required prerequisites block your progress.
Relationships: solid line = required · dashed line = recommended · dotted line = reinforcement.