Trigonometric Identities Study Cards

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Pythagorean Identities

A set of trigonometric identities that are derived from the Pythagorean theorem, involving the sine, cosine, and tangent functions.

Reciprocal Identities

A set of trigonometric identities that express the reciprocal relationships between the sine, cosine, tangent, cosecant, secant, and cotangent functions.

Quotient Identities

A set of trigonometric identities that express the quotient relationships between the sine, cosine, and tangent functions.

Co-Function Identities

A set of trigonometric identities that express the relationships between the trigonometric functions and their complementary angles.

Even-Odd Identities

A set of trigonometric identities that describe the even and odd properties of the trigonometric functions.

Sum and Difference Identities

A set of trigonometric identities that express the sum and difference relationships between the sine, cosine, and tangent functions.

Double Angle Identities

A set of trigonometric identities that express the relationships between the trigonometric functions of double angles.

Half Angle Identities

A set of trigonometric identities that express the relationships between the trigonometric functions of half angles.

Product-to-Sum Identities

A set of trigonometric identities that express the product of two trigonometric functions as a sum of trigonometric functions.

Sum-to-Product Identities

A set of trigonometric identities that express the sum of two trigonometric functions as a product of trigonometric functions.

Cofunction Identities

A set of trigonometric identities that express the relationships between the trigonometric functions and their cofunctions.

Inverse Trigonometric Identities

A set of trigonometric identities that express the relationships between the trigonometric functions and their inverse functions.

Hyperbolic Identities

A set of trigonometric identities that involve the hyperbolic functions, which are analogs of the trigonometric functions for hyperbolic angles.

Inverse Hyperbolic Identities

A set of trigonometric identities that express the relationships between the hyperbolic functions and their inverse functions.

Power-Reducing Identities

A set of trigonometric identities that express the powers of trigonometric functions in terms of lower powers.

Angle-Sum and Angle-Difference Identities

A set of trigonometric identities that express the relationships between the trigonometric functions of the sum and difference of two angles.

Cofunction Angle Identities

A set of trigonometric identities that express the relationships between the trigonometric functions of complementary angles.

Law of Sines

A trigonometric law that relates the lengths of the sides of a triangle to the sines of its angles.

Law of Cosines

A trigonometric law that relates the lengths of the sides of a triangle to the cosine of one of its angles.

Law of Tangents

A trigonometric law that relates the tangents of two angles of a triangle to the ratio of the lengths of the opposite and adjacent sides.

Law of Cotangents

A trigonometric law that relates the cotangents of two angles of a triangle to the ratio of the lengths of the adjacent and opposite sides.

Law of Secants

A trigonometric law that relates the secants of two angles of a triangle to the ratio of the lengths of the hypotenuse and adjacent side.

Law of Cosecants

A trigonometric law that relates the cosecants of two angles of a triangle to the ratio of the lengths of the hypotenuse and opposite side.

Euler's Formula

A mathematical formula that establishes the relationship between the exponential function, trigonometric functions, and imaginary numbers.

De Moivre's Theorem

A theorem that relates the powers of a complex number to its trigonometric form.

Trigonometric Equations

Equations that involve trigonometric functions and are solved using trigonometric identities and properties.

Trigonometric Graphs

Graphs that represent the values of trigonometric functions as angles vary.

Trigonometric Functions

Mathematical functions that relate the angles of a triangle to the lengths of its sides.

Trigonometric Ratios

The ratios of the lengths of the sides of a right triangle, which are used to define the trigonometric functions.

Trigonometric Formulas

Mathematical formulas that express relationships between the trigonometric functions.

Trigonometric Proofs

Proofs that demonstrate the validity of trigonometric identities and formulas.

Trigonometric Substitutions

Techniques used in calculus to simplify integrals involving trigonometric functions.

Trigonometric Integrals

Integrals that involve trigonometric functions and are solved using trigonometric identities and techniques.

Trigonometric Limits

Limits that involve trigonometric functions and are evaluated using trigonometric identities and properties.

Trigonometric Series

Infinite series that involve trigonometric functions and are used to represent periodic functions.

Trigonometric Derivatives

Derivatives of trigonometric functions, which are used in calculus to analyze the rates of change of trigonometric functions.

Trigonometric Inverses

Inverse functions of trigonometric functions, which are used to solve equations involving trigonometric functions.

Trigonometric Applications

Practical applications of trigonometry in various fields such as physics, engineering, and navigation.

Trigonometric Identities in Complex Numbers

Trigonometric identities that involve complex numbers and are used in complex analysis.

Trigonometric Identities in Calculus

Trigonometric identities that are used in calculus to simplify expressions and solve problems.

Trigonometric Identities in Geometry

Trigonometric identities that are used in geometry to solve problems involving angles and triangles.

Trigonometric Identities in Physics

Trigonometric identities that are used in physics to describe and analyze physical phenomena.

Trigonometric Identities in Engineering

Trigonometric identities that are used in engineering to solve problems related to structures, forces, and motion.

Trigonometric Identities in Computer Science

Trigonometric identities that are used in computer science to solve problems related to graphics, animation, and signal processing.

Trigonometric Identities in Statistics

Trigonometric identities that are used in statistics to analyze data and make predictions.

Trigonometric Identities in Finance

Trigonometric identities that are used in finance to calculate interest, investment returns, and risk.