Trigonometry Calculators

Degrees, radians and exact values

Every calculator in this section accepts angles in degrees or radians and keeps exact values such as $\frac{\sqrt{3}}{2}$ wherever they exist. The unit circle calculator explains the reference angle, the quadrant and the sign of each function, so you can find values like $\sin 150°$ without memorizing a table. For angles without a simple exact value, a decimal approximation is given and clearly marked.

Identities are checked rather than assumed. The identity calculator rewrites both sides with standard identities and also tests the equation numerically at many angles, so you learn whether an identity is true before you spend time proving it.

Solving triangles

Right triangles need only SOH-CAH-TOA, but most real problems involve triangles without a right angle. The law of cosines connects three sides and one angle, which makes it the tool for side-side-side and side-angle-side information. The calculator shows the formula with your numbers substituted, then finds the remaining angles and checks that they add up to $180°$.

These skills appear in physics, navigation, surveying and engineering, where angles and distances are measured and the missing values must be calculated.

A quick sketch prevents most mistakes. Label the sides opposite each angle with the matching lowercase letter, check that the largest side faces the largest angle, and make sure your calculator is in the same mode, degrees or radians, as the angles in the problem.