Trigonometry Calculator

Calculate sine, cosine and tangent, and solve any triangle with real-time SVG visualisation.

📐 Trigonometric functions
Angle in degrees
📏 Triangle solver
📋 Notable angles table
AngleRadianssincostan
0°0010
30°π/61/2√3/2√3/3
45°π/4√2/2√2/21
60°π/3√3/21/2√3
90°π/210∞
120°2π/3√3/2−1/2−√3
135°3π/4√2/2−√2/2−1
150°5π/61/2−√3/2−√3/3
180°π0−10

How to use the calculator

The calculator has two independent modules. The first calculates all six trigonometric functions (sine, cosine, tangent and their inverses) for any angle, in degrees or radians. The second solves complete triangles given three sufficient pieces of data, and draws the resulting triangle as a scalable SVG.

Module 1: basic trigonometric functions

Enter the angle and select the unit. The calculator returns sin, cos, tan, arcsin(sin), arccos(cos) and arctan(tan), plus the automatic conversion between degrees and radians. The angle can be any real number, positive or negative.

Module 2: triangle solver

Choose the case based on the data you know. The sides are labelled a, b and c, and the angles opposite them A, B and C (so A + B + C = 180°). The five available cases are:

The result shows all three sides, all three angles, the area and the perimeter. When the SSA case has two valid solutions, the calculator shows both of them.

Fundamental laws of trigonometry

Law of sines

In any triangle, the ratio of each side to the sine of the opposite angle is constant and equal to the diameter of the circumscribed circle:

a / sin(A) = b / sin(B) = c / sin(C) = 2R

Applied in the AAS, ASA and SSA cases. In the SSA case it can yield two possible angles (one acute and one obtuse), hence the name "ambiguous case".

Law of cosines

Generalises the Pythagorean theorem to any triangle:

a² = b² + c² − 2·b·c·cos(A)

Applied in the SAS and SSS cases. When A = 90°, the term 2bc·cos(A) is zero and the Pythagorean theorem is recovered.

Frequently asked questions

How do you calculate the sine of an angle?
The sine of an angle in a right triangle is the ratio of the opposite side to the hypotenuse: sin(α) = opposite / hypotenuse. To calculate the sine of any angle in degrees use this calculator: enter the angle and click Calculate. Internally it converts to radians before applying the mathematical function: rad = degrees × π / 180.
What is the law of sines?
The law of sines states that in any triangle, the ratio of each side to the sine of the opposite angle is constant: a/sin(A) = b/sin(B) = c/sin(C). It is used to solve triangles when two angles and a side are known (AAS or ASA), or two sides and a non-included angle (SSA, the ambiguous case).
What is the law of cosines and when is it used?
The law of cosines generalises the Pythagorean theorem: a² = b² + c² − 2bc·cos(A). It is used when all three sides are known (SSS) to find the angles, or when two sides and the included angle are known (SAS) to find the third side and remaining angles.
What are the exact values of sine and cosine at 30°, 45° and 60°?
The exact values are: sin(30°)=1/2, cos(30°)=√3/2; sin(45°)=√2/2, cos(45°)=√2/2; sin(60°)=√3/2, cos(60°)=1/2. These values are frequently used in exams and geometry problems because they are exact fractions, not approximated decimals.
What is the difference between degrees and radians?
Degrees divide the full circle into 360 equal parts, while radians measure angles as the arc length on a unit circle. The equivalence is: 180° = π radians ≈ 3.14159 rad. Radians are used internally in mathematics and programming because they simplify the formulas of differential calculus.
How do you solve a triangle with two sides and an angle?
It depends on whether the angle is included between the two sides (SAS case) or opposite to one of them (SSA case). In the SAS case the law of cosines gives the third side and then the law of sines gives the remaining angles. In the SSA case (ambiguous case) there can be 0, 1 or 2 possible triangles: this calculator shows both solutions when they exist.
What is trigonometry used for in real life?
Trigonometry is used in architecture and construction to calculate roof angles and slopes; in surveying to measure inaccessible distances; in navigation (GPS, aviation) to compute trajectories; in graphic design and video games for rotations and 3D projections; and in electrical engineering to analyse alternating currents and audio signals.

Last updated

Calculator updated in 2026. Compatible with all modern browsers without installing any extension or app.