Trigonometry: A Complete Guide
Trigonometry is the branch of mathematics that studies relationships between the sides and angles of triangles. It extends to the study of periodic functions through the unit circle. This calculator covers the three main use cases: right triangles, oblique triangles, and the unit circle.
Solving Methods
Right Triangle
With one 90-degree angle, use Pythagorean theorem and basic trig ratios.
a^2 + b^2 = c^2, sin A = a/c
Law of Sines
For oblique triangles: relates sides to their opposite angles.
a/sin(A) = b/sin(B) = c/sin(C)
Law of Cosines
Generalization of Pythagorean theorem for any triangle.
c^2 = a^2 + b^2 - 2ab cos(C)
Unit Circle
Circle with radius 1, centered at origin. Defines trig functions for all angles.
(cos(x), sin(x)) on the circle
Tips for Solving Triangles
- Always check that the sum of angles equals 180 degrees.
- For right triangles, you only need 2 values (one must be a side).
- For oblique triangles, you need 3 values (at least one side).
- SSA (two sides and non-included angle) can give 0, 1, or 2 solutions (ambiguous case).