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Lecture# Trigonometric Equations: Basics

Description

This lecture covers the basics of trigonometric equations, including simple trigonometric equations like sin x = sin a, solving equations over specific intervals, transformation techniques, and factorization methods. The examples presented demonstrate the application of these concepts in solving equations involving trigonometric functions. The instructor illustrates the step-by-step process of solving equations such as sin(2x) = 3/4 and cos(3x + 2) = 2 cos(x) sin(-x), emphasizing the importance of domain definition and identifying solutions within specific intervals.

Official source

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In MOOCs (2)

Trigonometric Functions, Logarithms and Exponentials

Ce cours donne les connaissances fondamentales liées aux fonctions trigonométriques, logarithmiques et exponentielles. La présentation des concepts et des propositions est soutenue par une grande gamm

Trigonometric Functions, Logarithms and Exponentials

Ce cours donne les connaissances fondamentales liées aux fonctions trigonométriques, logarithmiques et exponentielles. La présentation des concepts et des propositions est soutenue par une grande gamm

Related concepts (61)

Instructor

Trigonometric functions

In mathematics, the trigonometric functions (also called circular functions, angle functions or goniometric functions) are real functions which relate an angle of a right-angled triangle to ratios of two side lengths. They are widely used in all sciences that are related to geometry, such as navigation, solid mechanics, celestial mechanics, geodesy, and many others. They are among the simplest periodic functions, and as such are also widely used for studying periodic phenomena through Fourier analysis.

Inverse trigonometric functions

In mathematics, the inverse trigonometric functions (occasionally also called arcus functions, antitrigonometric functions or cyclometric functions) are the inverse functions of the trigonometric functions (with suitably restricted domains). Specifically, they are the inverses of the sine, cosine, tangent, cotangent, secant, and cosecant functions, and are used to obtain an angle from any of the angle's trigonometric ratios. Inverse trigonometric functions are widely used in engineering, navigation, physics, and geometry.

List of trigonometric identities

In trigonometry, trigonometric identities are equalities that involve trigonometric functions and are true for every value of the occurring variables for which both sides of the equality are defined. Geometrically, these are identities involving certain functions of one or more angles. They are distinct from triangle identities, which are identities potentially involving angles but also involving side lengths or other lengths of a triangle. These identities are useful whenever expressions involving trigonometric functions need to be simplified.

Exact trigonometric values

In mathematics, the values of the trigonometric functions can be expressed approximately, as in , or exactly, as in . While trigonometric tables contain many approximate values, the exact values for certain angles can be expressed by a combination of arithmetic operations and square roots. The trigonometric functions of angles that are multiples of 15°, 18°, or 22.5° have simple algebraic values. These values are listed in the following table for angles from 0° to 90°.

Logarithmic scale

A logarithmic scale (or log scale) is a way of displaying numerical data over a very wide range of values in a compact way. As opposed to a linear number line in which every unit of distance corresponds to adding by the same amount, on a logarithmic scale, every unit of length corresponds to multiplying the previous value by the same amount. Hence, such a scale is nonlinear: the numbers 1, 2, 3, 4, 5, and so on, are not equally spaced. Rather, the numbers 10, 100, 1000, 10000, and 100000 would be equally spaced.

Related lectures (661)

Continuity of Trigonometric FunctionsMOOC: Trigonometric Functions, Logarithms and Exponentials

Explores the continuity of trigonometric functions and demonstrates specific limits and propositions related to them.

Trigonometric Equations: Sinus and CosinusMOOC: Trigonometric Functions, Logarithms and Exponentials

Covers the resolution of simple trigonometric equations involving sinus and cosinus functions.

Harmonic Oscillations: SuperpositionMOOC: Trigonometric Functions, Logarithms and Exponentials

Explores the principle of superposition for harmonic oscillations and provides geometric interpretations and examples.

Cosine TheoremMOOC: Trigonometric Functions, Logarithms and Exponentials

Explores the cosine theorem in triangles, analyzing side and angle relationships.

Trigonometric Formulas: Addition TheoremMOOC: Trigonometric Functions, Logarithms and Exponentials

Explores trigonometric addition theorem, double angles, and tangent properties.