Live measurements
- Angle
- 30.0 °
- Angle
- 0.52 rad
- cos θ · x-coordinate
- 0.87
- sin θ · y-coordinate
- 0.50
- Quadrant (0 = axis)
- 1.00
- Reference angle
- 30.0 °
MathematicsGCSE & A-Level8 minBeta
Unit Circle & Exact Values Explorer
Move through a full turn and connect angle, quadrant, reference angle and the point (cos θ, sin θ), with exact values shown at standard angles.
Model presets
Reviewed starting statesCurriculum map
- AQA GCSE Mathematics
Geometry and Measures → Exact trigonometric values - AQA A-Level Mathematics
Trigonometry → Radians, identities and exact values
Model boundaries
- Angles are measured anticlockwise from the positive x-axis.
- The diagram uses a unit radius, so horizontal and vertical coordinates equal cosine and sine.
- Exact radical labels are supplied for standard 30°, 45°, 60° and axis-related angles; other 15° steps use decimals.
StudyVector-authored unit-circle model using exact standard-angle values and deterministic trigonometric coordinates; mapped to the curriculum topics shown below.
Accessible text description
A coordinate plane contains a unit circle with four labelled quadrants. A radius arm ends at the point (cos θ, sin θ). Dashed horizontal and vertical projections form a reference triangle, while sign labels and an exact-value readout connect the selected standard angle to its coordinates. Native 15-degree step buttons duplicate the slider interaction.