Trig Identities Calculator

Verify trigonometric identities numerically. Select a category, enter an angle, and see each identity verified.

Identity Category

Identity Verification

Pythagorean Identities
All Verified
sin^2(x) + cos^2(x) = 1

Trigonometric Identities

Trigonometric identities are equations involving trig functions that are true for all values of the variable where both sides are defined. They are essential tools for simplifying expressions, solving equations, and proving other mathematical results.

Categories of Identities

Pythagorean Identities

Based on the Pythagorean theorem applied to the unit circle.

sin^2(x) + cos^2(x) = 1

Double Angle

Express trig functions of 2x in terms of functions of x.

sin(2x) = 2 sin(x) cos(x)

Half Angle

Express trig functions of x/2 in terms of functions of x.

sin(x/2) = +/-sqrt((1-cos(x))/2)

Sum / Difference

Express trig functions of (A+/-B) in terms of A and B.

sin(A+B) = sinA cosB + cosA sinB

Why Verify Identities Numerically?

While trig identities hold for all valid angles, verifying them numerically for a specific angle is a useful learning tool. It helps build intuition about how the identities work and can serve as a sanity check when solving problems. This calculator evaluates both sides of each identity and confirms they match within floating-point precision.

Common Uses

  • Simplifying trigonometric expressions in calculus
  • Solving trigonometric equations
  • Signal processing and Fourier analysis
  • Physics problems involving waves and oscillations