Convert Angles Using a Half-Turn Equivalence
A half turn is both 180 degrees and π radians.
About 25 minutes, plus any extended practice
Open lesson 1Precalculus: Radians and the Unit Circle
Radians measure an angle by arc length relative to radius. On the unit circle, cosine and sine are horizontal and vertical coordinates, so quadrant signs and special triangles support exact values beyond acute angles.
Before you begin
- Use fractions of π; know right-triangle sine and cosine; read signed Cartesian coordinates.
Choose by skill rather than age alone. Read with an adult when useful, revisit a lesson, or explore another grade.
Follow the lesson sequence
Find Exact Coordinates from a Special Reference Angle
The unit-circle point at angle θ is (cosθ,sinθ).
About 25 minutes, plus any extended practice
Open lesson 2Calculate Tangent from Sine and Cosine
Tangent is sine divided by cosine wherever cosine is nonzero.
About 25 minutes, plus any extended practice
Open lesson 3Read Sine and Cosine Signs from Coordinates
Quadrant location fixes the signs of a point’s horizontal and vertical coordinates.
About 25 minutes, plus any extended practice
Open lesson 4Review and transfer
After the lessons, try 4 new review cases and a practical task. Each answer has an explanation and a link back to the related lesson.
Open the unit reviewGuest answers are temporary. Keep your own paper or document; this unit does not certify completion or record a school grade.
Topic references
- OpenStax mathematical topic reference: topic reference — Precalculus: Radians and the Unit Circle
These references informed the topic selection. They do not certify complete standards alignment.