Trigonometry Calculator
Calculate Sin, Cos, Tan & Visualize the Unit Circle.
Degrees (°)
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90°
180°
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Current Quadrant: I
All Positive
All Positive
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Visual Representation
0.785 rad (π/4)
Trigonometric Ratios
Sin θ
0.707
Cos θ
0.707
Tan θ
1.000
Csc θ
1.414
Sec θ
1.414
Cot θ
1.000
What is Trigonometry?
[Image of unit circle diagram with sin cos]Trigonometry is the branch of mathematics that studies the relationships between the side lengths and angles of triangles. It is fundamental to geometry, physics, engineering, and even video game development.
SOH CAH TOA (The Golden Rule)
This is the easiest way to remember the definitions of the three main ratios based on a right-angled triangle:
- SOH: Sine = Opposite / Hypotenuse
- CAH: Cosine = Adjacent / Hypotenuse
- TOA: Tangent = Opposite / Adjacent
The Unit Circle Explained
The Unit Circle is a circle with a radius of exactly 1 unit, centered at the origin (0,0). It is a powerful tool to understand trigonometry beyond 90 degrees.
- The X-coordinate of any point on the circle is cos(θ).
- The Y-coordinate of any point on the circle is sin(θ).
Our interactive visualizer above shows exactly this. The blue horizontal line represents Cosine, and the red vertical line represents Sine.
Standard Angles Table
| Angle | 0° | 30° | 45° | 60° | 90° |
|---|---|---|---|---|---|
| Sin | 0 | 0.5 | 0.707 | 0.866 | 1 |
| Cos | 1 | 0.866 | 0.707 | 0.5 | 0 |
| Tan | 0 | 0.577 | 1 | 1.732 | ∞ |