Trigonometry Calculator

Engineering and Physics

Engineers use trigonometry for structural analysis, wave mechanics, signal processing, and mechanical design. Physics applications include oscillatory motion, electromagnetic waves, quantum mechanics, and celestial mechanics calculations.

Navigation and Surveying

Navigation systems use trigonometry for GPS calculations, bearing determination, and distance measurement. Surveyors apply trigonometric principles for land measurement, mapping, construction layout, and topographical analysis.

Computer Graphics and Animation

Computer graphics rely on trigonometry for 3D transformations, rotation calculations, lighting effects, and animation paths. Game development uses trigonometric functions for character movement, physics simulations, and visual effects.

Fundamental Identities

Key trigonometric identities include Pythagorean identities (sin²θ + cos²θ = 1), reciprocal identities (csc = 1/sin), and quotient identities (tan = sin/cos). These relationships are essential for simplifying expressions and solving equations.

Angle Addition Formulas

Angle addition formulas allow calculation of trigonometric functions for compound angles. Examples include sin(A + B) = sinA cosB + cosA sinB and cos(A + B) = cosA cosB - sinA sinB, useful for complex angle calculations.

Special Angle Values

Common special angles include 30°, 45°, and 60° (π/6, π/4, π/3 radians). These angles have exact trigonometric values: sin(30°) = 1/2, cos(45°) = √2/2, tan(60°) = √3, which are frequently used in calculations.

Inverse Functions

Inverse trigonometric functions (arcsin, arccos, arctan) find angles when function values are known. These functions have restricted domains and ranges to ensure unique solutions and are essential for solving triangles and angle determination problems.