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Lecture# Trigonometric Functions: Sin and Cos

Description

This lecture covers the definition of trigonometric functions, specifically the sine and cosine functions, and their inverses. It explains how these functions are related to the unit circle, introduces the notation for sine and cosine, defines the functions, provides examples of their values, and discusses the Pythagorean relation. The lecture also explores the graphs of the sine function, notable points on the sine curve, the behavior of sine and cosine in terms of growth and decline, and concludes with a summary of the key concepts learned.

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In MOOCs (2)

Related concepts (63)

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

Sine and cosine

In mathematics, sine and cosine are trigonometric functions of an angle. The sine and cosine of an acute angle are defined in the context of a right triangle: for the specified angle, its sine is the ratio of the length of the side that is opposite that angle to the length of the longest side of the triangle (the hypotenuse), and the cosine is the ratio of the length of the adjacent leg to that of the hypotenuse. For an angle , the sine and cosine functions are denoted simply as and .

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.

Lausanne

Lausanne (loʊˈzæn , USalsoloʊˈzɑːn , lɔzan; Losena lɔˈzəna) is the capital and largest city of the Swiss French-speaking canton of Vaud. It is a hilly city situated on the shores of Lake Geneva, about halfway between the Jura Mountains and the Alps, and facing the French town of Évian-les-Bains across the lake. Lausanne is located northeast of Geneva, the nearest major city. The municipality of Lausanne has a population of about 140,000, making it the fourth largest city in Switzerland after Basel, Geneva, and Zurich, with the entire agglomeration area having about 420,000 inhabitants (as of January 2019).

Lausanne District

Lausanne District (District de Lausanne) is a district in the canton of Vaud, Switzerland. The seat of the district is the city of Lausanne. Lausanne has an area, , of . Of this area, or 27.3% is used for agricultural purposes, while or 30.9% is forested. Of the rest of the land, or 41.6% is settled (buildings or roads) and or 0.1% is unproductive land. Lausanne has a population () of . Most of the population () speaks French (159,559 or 79.6%), with German being second most common (8,534 or 4.

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

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Introduces trigonometric functions in right triangles, exploring angles, ratios, and special values.

Continuity of Trigonometric FunctionsMOOC: Trigonometric Functions, Logarithms and Exponentials

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