Extending angles

Interpret angles as rotations and connect degrees, radians, and unit-circle positions.

Meaning

General angles describe rotational direction and amount from a starting direction; they may exceed a full turn or be negative. Radians measure angle as arc length divided by radius.

Example

An arc of length 3 on a circle of radius 3 subtends 1 radian. A full turn is radians, so 180 degrees is radians.A full turn has arc length 2πr, so dividing by radius r gives 2π. Scaling a circle scales arc length and radius equally, preserving the radian measure of a fixed angle.Do not mix radians and degrees. 1 radian is about 57.3 degrees, not 1 degree.

Practice for this concept

Scope and references

Topics

General angles, radian measure, unit circles

Learning goal

Interpret angles as rotations and connect degrees, radians, and unit-circle positions.

Helpful background

Explore rotation, radii, and arcs.

Extended angles

These ordinary choice questions provide limited practice in this concept. They do not establish independent solution, full-concept performance, or mastery.

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