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Learn about the equalities that involve trigonometric functions and are true for every value of the variables. Find the Pythagorean, reciprocal, reflection, shift, periodicity, angle sum and difference, and Ptolemy identities with examples and proofs.
Learn how to prove various identities involving trigonometric functions using geometry, algebra, calculus, and Euler's formula. The article covers elementary, angle sum, double-angle, half-angle, and sum to product identities, as well as inequalities and compositions of trig and inverse trig functions.
The law of cotangents is a trigonometric identity that relates the sides and angles of a triangle to the cotangents of half the angles. Learn the statement, proof, and applications of this law, as well as other related identities.
Secant is one of the six trigonometric functions that relate an angle of a right triangle to ratios of two side lengths. Learn how to define secant using a right triangle, a unit circle, or a differential equation, and how it relates to other trigonometric functions.
Learn how to remember trigonometric identities and functions using mnemonics, such as SOH-CAH-TOA and All Students Take Calculus. Find out the signs of trigonometric functions in each quadrant and the sines and cosines of special angles.
Learn how to relate the tangent of half an angle to trigonometric functions of the entire angle using various formulas, proofs, and applications. Find out how the tangent half-angle formula can be used in calculus, hyperbolic functions, and rational values.
Learn about the inverse functions of the trigonometric functions, such as arcsin, arccos, and arctan, and how they are used in mathematics and engineering. Find the definitions, domains, ranges, and properties of the inverse trigonometric functions.
Learn how to use trigonometric identities to simplify integrals involving radical functions. See examples of different cases, geometric constructions, and substitutions of hyperbolic functions.