Trigonometría y geometría analítica

Go to Course: https://www.coursera.org/learn/trigonometria

Introduction

### Course Review: Trigonometría y Geometría Analítica on Coursera #### Course Overview **Name**: Trigonometría y Geometría Analítica **Platform**: Coursera **Language**: Spanish The course "Trigonometría y Geometría Analítica" offers a comprehensive exploration of fundamental concepts in trigonometry and analytic geometry. This course is structured into two main modules, focusing initially on the principles and applications of trigonometry, followed by an in-depth look at analytic geometry, emphasizing conic sections such as lines, parabolas, circles, and ellipses, and their practical applications. #### Course Syllabus Breakdown 1. **Elementos de Trigonometría** Trigonometry is presented in a relatable context, demonstrating its importance in everyday life. The module addresses real-world problems related to measurement, such as calculating the area of land, measuring heights of inaccessible objects, and understanding road inclines. The hands-on approach empowers you to tackle these challenges, dispelling the notion that only engineers or mathematicians possess the necessary skills. 2. **Elementos Básicos de Geometría Analítica** This module lays the groundwork for analytic geometry by teaching how to represent points and segments on the Cartesian plane. With a focus on geometric locations, students engage in exercises to practice both algebraic and graphical methods, developing a strong foundational understanding of the subject. 3. **La Recta y Su Ecuación Cartesiana** In this segment, learners dive into the various forms of line equations, revealing the algebraic structure that underlies many geometric characteristics and parameters. The insights gained here prove invaluable for understanding more complex geometric concepts. 4. **La Parábola y Su Ecuación Cartesiana** This module introduces parabolas, guiding participants through their canonical and general forms, including vertices located at the origin and elsewhere. Practical applications are emphasized, providing context and relevance to the mathematical theories explored. 5. **La Circunferencia, La Elipse y Sus Ecuaciones Cartesianas** The final module discusses the properties of circles and ellipses as geometric locations, allowing students to synthesize what they've learned regarding Cartesian equations to solve algebraic and graphical problems related to these shapes. #### Course Evaluation **Strengths**: - **Practical Relevance**: Each module applies theoretical knowledge to practical situations, making the content applicable and engaging for learners. - **Structured Learning**: The course is logically structured, transitioning smoothly from trigonometry to analytic geometry. - **Interactive Exercises**: The inclusion of exercises enhances understanding and retention of concepts, providing learners with opportunities to apply their knowledge. **Potential Areas for Improvement**: - **Language Limitations**: Currently offered in Spanish, which may limit accessibility for non-Spanish speakers. Future options for subtitles in other languages could broaden its reach. - **Additional Advanced Topics**: While the course covers fundamental concepts thoroughly, an introduction to more advanced applications of trigonometry and analytic geometry could appeal to a wider audience. #### Recommendation I highly recommend "Trigonometría y Geometría Analítica" for anyone looking to enhance their understanding of these crucial mathematical concepts, especially students and professionals in fields that require practical measurement and geometric reasoning. The course's relevance to real-life scenarios ensures that learners not only grasp theoretical aspects but are also equipped to apply these skills meaningfully. Whether you're looking to solidify your foundation in mathematics or tackle specific problems in daily life, this course is an excellent resource that offers both knowledge and confidence in handling trigonometric and geometric challenges. Embark on this mathematical journey on Coursera, and unlock the potential of trigonometry and analytic geometry in both your personal and professional life!

Syllabus

Elementos de trigonometría

En la vida cotidiana muchas veces se presentan problemas de medición. Por ejemplo, conocer la superficie de un terreno, ya sea que lo vamos a vender o comprar, medir la altura de algún objeto que no es accesible fácilmente, saber la inclinación de una carretera, etc. ¿Sólo pueden resolver estos problemas los ingenieros o matemáticos? No, pues como aprenderás aquí, tú también podrás hacerlo con base en el estudio de la trigonometría.

En este módulo se tratarán conceptos básicos de geometría analítica, el uso del plano cartesiano para representar puntos, segmentos y el concepto de lugar geométrico, junto con algunos ejemplos y ejercicios con los que puedes practicar el método algebraico y gráfico en un sistema de coordenadas.

En este módulo obtendrás las ecuaciones de la recta en algunas de sus formas, cuya estructura algebraica permite deducir una gran parte sus características geométricas, así como sus parámetros.

En este módulo obtendrás las ecuaciones de la parábola en sus formas canónica u ordinaria tanto con vértice en el origen como fuera de él, y transitarás de la forma canónica a la forma general y viceversa, además de que aplicarás la parábola en la solución de problemas reales.

En este módulo se describirán los conceptos de circunferencia y elipse como lugares geométricos para lograr definir las propiedades, aplicaciones y problemas de manera algebraica y gráfica con base en el uso de sus ecuaciones cartesianas.