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Unit Circle & Exact Values Explorer — Interactive Mathematics | StudyVector

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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

Authored starting states

StudyVector model lab

Angular relationship scope

Model inputs: 2 inputs
Visible model layers: 4/4 layers
Model state: State-linked

Live model readout

Updates with every input

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 °

Curriculum 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.