# Trigonometría y geometría analítica

Universidad Nacional Autónoma de México

Embark on a captivating journey through the realms of trigonometry and analytical geometry with the course "Trigonometría y geometría analítica." This comprehensive offering, presented by Universidad Nacional Autónoma de México, invites participants to immerse themselves in the intricate world of trigonometry and its practical applications in real-life scenarios. The course's initial module unfolds the historical backdrop and the fundamental concepts of trigonometry, steering learners through the exploration of trigonometric ratios, identities, and oblique triangles. The subsequent module delves into the intricacies of analytical geometry, elucidating the basics of the Cartesian plane, length, slope, and angle of inclination. Moreover, participants will gain insights into special points of line segments, the midpoint of a line segment, and geometric loci on the Cartesian plane.

The course further navigates the terrain of geometric shapes, dissecting the equations of lines, parabolas, circles, and ellipses. Learners will unravel the nuances of rectilinear equations, various forms of the line equation, and the angles formed between lines. Additionally, they will delve into the construction, definition, and equations of parabolas, exploring their applications in diverse contexts. The course culminates with an exploration of the circular and elliptical shapes, illustrating their geometric properties and equations.

Encompassing a rich blend of theoretical principles and practical applications, this course equips participants with a profound understanding of trigonometry and analytical geometry, enabling them to apply these concepts to everyday situations and real-world problems.

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##### Course Modules

This course comprises in-depth modules covering trigonometry, analytical geometry, line equations, parabolas, circles, and ellipses, offering practical insights into the application of mathematical principles in real-life scenarios.

#### Elementos de trigonometría

The first module of the course delves into the historical evolution and fundamental concepts of trigonometry, elucidating trigonometric ratios, identities, and their applications in oblique triangles. Participants will explore the practical utility of trigonometry in everyday life, gaining a comprehensive understanding of its significance and origins.

#### Elementos básicos de geometría analítica

Embarking on the second module, participants will delve into the intricacies of analytical geometry, navigating through the basics of the Cartesian plane, length, slope, and angle of inclination. They will explore special points of line segments, the midpoint of a segment, and the geometric loci on the Cartesian plane, gaining practical insights into their applications.

#### La recta y su ecuación cartesiana

The third module unravels the dynamics of line equations, encompassing various forms and equations of lines. Participants will explore angles formed between lines and the practical application of line equations in solving Euclidean geometry problems, gaining a comprehensive understanding of rectilinear equations and their significance.

#### La parábola y su ecuación cartesiana

Delving into the fourth module, participants will dissect the construction, definition, and equations of parabolas, including their diverse applications in real-life scenarios. They will gain insights into the geometric properties, equations, and practical implications of parabolas, unraveling their significance in modern life.

#### La circunferencia, la elipse y sus ecuaciones cartesianas

The final module navigates through the circular and elliptical shapes, elucidating their geometric properties and equations. Participants will gain practical insights into the applications of circles and ellipses, unraveling their significance in diverse contexts and problem-solving scenarios.

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