Trig calculator
All six trigonometric functions for any angle, and the inverse functions for any ratio, in degrees or radians.
Why sine and cosine are just coordinates
Put a point on a circle of radius 1 and turn it by an angle θ from the positive x-axis. Its x-coordinate is cos θ and its y-coordinate is sin θ. Tangent is the slope of the radius: sin ÷ cos. Drag the slider and watch the signs change as you cross each quadrant.
Because x² + y² = 1 on this circle, sin²θ + cos²θ = 1 for every angle. At 90° the radius is vertical, cos is 0 and tan is undefined.
Exact values of common angles
| Degrees | Radians | sin | cos | tan |
|---|---|---|---|---|
| 0° | 0 | 0 | 1 | 0 |
| 30° | π/6 | 1/2 | √3/2 | √3/3 |
| 45° | π/4 | √2/2 | √2/2 | 1 |
| 60° | π/3 | √3/2 | 1/2 | √3 |
| 90° | π/2 | 1 | 0 | undefined |
| 180° | π | 0 | −1 | 0 |
| 270° | 3π/2 | −1 | 0 | undefined |
| 360° | 2π | 0 | 1 | 0 |
The identities worth knowing
- sin²θ + cos²θ = 1 (Pythagorean identity)
- tan θ = sin θ / cos θ
- sin(−θ) = −sin θ, cos(−θ) = cos θ
- sin(90° − θ) = cos θ (co-function)
- sin 2θ = 2 sin θ cos θ
- cos 2θ = cos²θ − sin²θ
Solving a triangle rather than a single angle? The triangle calculator applies the law of sines and cosines for you.
Show me the steps
An AI tutor walks through the working for this exact result. The answer above is computed in your browser; the explanation is optional and is the only thing that leaves your device.
Find sin, cos and tan of 30 degrees = sin = 0.5, cos = 0.8660254038, tan = 0.5773502692
Questions people ask
Should I use degrees or radians?
Use degrees if the angle came from a protractor, a drawing or a surveying problem. Use radians in calculus, physics formulas like ω = 2πf, and code. Getting this wrong is the most common reason a trig answer looks nonsensical: sin(30) is 0.5 in degrees but −0.988 in radians.
What is the difference between sin⁻¹ and 1/sin?
sin⁻¹ (arcsin) is the inverse function: it takes a ratio and returns an angle. 1/sin is the reciprocal, called cosecant (csc). They are completely different, despite the confusing notation.
Why does arcsin only give one answer?
Many angles share the same sine (sin 30° = sin 150° = 0.5). Inverse functions return the principal value: arcsin gives −90° to 90°, arccos 0° to 180°, arctan −90° to 90°. Add or reflect by 180° or 360° to find the others.
Why is tan 90° undefined?
tan = sin/cos, and cos 90° = 0. Dividing by zero has no value, so the calculator reports undefined rather than a huge rounding artefact.
What does SOH CAH TOA mean?
A memory aid for right triangles: Sine = Opposite/Hypotenuse, Cosine = Adjacent/Hypotenuse, Tangent = Opposite/Adjacent. For solving whole triangles, use the triangle calculator.