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Mathematics
Unit Circle Toolkit
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Look up angles, compare, solve and practise on the unit circle.
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α = 30°
sin = 1/2cos = √3/2
Examples: −30; 45.5; 180/7. You can also press Enter to apply.
Angles in the current turn
Arrow keys: 1°; Shift: 0.1°; Page: 15°.
Display layers
α = 30°
= π/6 rad
- sin α
- = 1/2
- cos α
- = √3/2
- tan α
- = √3/3
- cot α
- = √3
- M(cos α; sin α)
- (√3/2; 1/2)
- Angle reduced to one turn
- 30°
- Signed complete turns / Signed remainder
- 0 / 30°
- Position
- Quadrant 1
- Reference angle
- 30°
Special angle table
Angles in the current turn
| α | sin | cos |
|---|---|---|
| = 0 | = 1 | |
| = 1/2 | = √3/2 | |
| = √2/2 | = √2/2 | |
| = √3/2 | = 1/2 | |
| = 1 | = 0 | |
| = √3/2 | = −1/2 | |
| = √2/2 | = −√2/2 | |
| = 1/2 | = −√3/2 | |
| = 0 | = −1 | |
| = −1/2 | = −√3/2 | |
| = −√2/2 | = −√2/2 | |
| = −√3/2 | = −1/2 | |
| = −1 | = 0 | |
| = −√3/2 | = 1/2 | |
| = −√2/2 | = √2/2 | |
| = −1/2 | = √3/2 | |
| = 0 | = 1 |
Reset clears the tool's inputs and practice session.
Model notes
- The circle has radius 1; angles may be negative or exceed one turn. Input bounds are tool limits, not mathematical limits.
- Tangent lines clipped at the frame can still represent finite values. ≈ indicates rounding; undefined points are handled separately.
- Substitution checks an example rather than proving an identity. The solver supports sin, cos, tan, cot of ax+b within the documented bounds.
- Session persistence depends on the host platform. Copy a situation code to keep your lookup inputs yourself.