Trigonometry
Trigonometry studies the relationships between the sides and angles of triangles, and the periodic functions that come out of those relationships. The tools on this page solve triangles in every standard configuration and evaluate every trig function in degrees or radians.
Two ideas do most of the heavy lifting in trigonometry. The first is that in a right triangle the ratios of sides depend only on the angle, giving us sin, cos and tan. The second is that those ratios extend to any triangle through the laws of sines and cosines. Once you have those, almost every triangle problem becomes routine.
Right triangles
Use the Pythagorean theorem for the sides and the inverse trig functions for the angles. The Right Triangle solver does both from any two pieces of information.
The six trig functions
sin, cos and tan are the primary ratios; csc, sec and cot are their reciprocals. The evaluator handles all six in degrees or radians and reports cleanly when a value is undefined.
Laws of sines and cosines
For any triangle, a/sin A = b/sin B = c/sin C (law of sines) and c² = a² + b² − 2ab·cos C (law of cosines). Pick the one that matches the data you have.
Angle conversions and reference angles
Every angle in standard position has a reference angle in the first quadrant; the converter gives this, the coterminal angle and the quadrant alongside the deg/rad conversion.
All solvers
Frequently asked questions
Are trig functions in degrees or radians?
Mathematically, the functions take radians; the tools let you enter either and convert internally.
What is a reference angle?
The acute angle between the terminal side of an angle and the x-axis — always between 0° and 90° — used to relate any angle to a first-quadrant value.
When should I use the law of sines vs the law of cosines?
Use the law of sines when you know an angle and its opposite side; use the law of cosines for two sides and the included angle, or all three sides.