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Trigonometría y geometría analítica
Mario Jiménez Velasco
and
Victoria Rojas López
Mario Jiménez Velasco
and
Victoria Rojas López
El curso Trigonometría y geometría analítica abordará en su primer módulo el estudio de la trigonometría y sus aplicaciones en casos prácticos. A partir del segundo módulo abordará el estudio de la geometría analítica, en particular, de las secciones cónicas: la recta, la parábola, la circunferencia y la elipse; así como sus aplicaciones en situaciones de la vida cotidiana.
Register for this course and see more details by visiting:
OpenCourser.com/course/nh213v/trigonometria
What's inside
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.
Read more
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.
Read more
Elementos básicos de geometría analítica
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.
La recta y su ecuación cartesiana
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.
La parábola y su ecuación cartesiana
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.
La circunferencia, la elipse y sus ecuaciones cartesianas
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.
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possible dealbreakers
Está orientado a estudiantes que desean fortalecer sus conocimientos en trigonometría y geometría analítica
Aborda conceptos básicos de geometría analítica, ecuaciones de la recta, parábola, circunferencia y elipse
Ofrece aplicaciones prácticas de la trigonometría y la geometría analítica
Es impartido por profesores experimentados, Mario Jiménez Velasco y Victoria Rojas López
Requiere conocimientos previos de matemáticas básicas
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Save Trigonometría y geometría analítica to your list so you can find it easily later:
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Reviews summary
Trigonometry and analytic geometry: accessible and practical
Trigonometry and Analytic Geometry is a well-structured and comprehensive course that provides a solid foundation in both trigonometry and analytic geometry. The course is accessible to students of varying levels, and the practical applications make the learning experience engaging. While there are a few minor issues with assessments and exercises, the overall quality of the course is excellent.
Appropriate for High School Students
"Es un excelente curso, ideal para estudiantes de bachillerato..."
Engaging and Practical
"Muy práctico y útil, es fácil de entender..."
Clear and Well-Organized
"Está muy bien estructurado y fácil para aprender."
"Me pareció muy bueno este curso porque aprendí con facilidad debido a su contenido y su orden."
Assessment Errors
"Había errores en las evaluaciones."
"Todo bien explicado. Sólo en algunas preguntas me parece que de la semana 1 y 2 hay unos errores en las respuesta."
Excessive Exercises
"podrían ser menos tareas, 2 por semana"
"desde la tercera semana se hacen demasiadas."
Activities
Be better prepared
before
your course. Deepen your understanding
during
and
after
it. Supplement your coursework and achieve mastery of the topics covered
in Trigonometría y geometría analítica with these
activities:
Explore Online Tutorials
Show steps
Supplements your learning with additional resources and expert guidance.
Show steps
-
Identify reputable online platforms or educators that offer tutorials on trigonometry and geometry.
-
Select tutorials that align with your learning objectives.
-
Follow the tutorials, take notes, and practice the concepts.
Revisit basic geometry
Show steps
Reinforces your understanding of geometric principles and their applications.
Browse courses on
Geometry
Show steps
-
Review the definitions and properties of basic geometric shapes, such as triangles, circles, and squares.
-
Solve problems involving angles, lengths, and areas of geometric shapes.
-
Identify and apply geometric concepts in real-world situations.
Trigonometric Identities Practice
Show steps
Strengthens your ability to manipulate and apply trigonometric identities.
Browse courses on
Trigonometry
Show steps
-
Memorize fundamental trigonometric identities (e.g., sin²x + cos²x = 1).
-
Practice using identities to solve trigonometric equations and simplify expressions.
-
Apply trigonometric identities to real-world applications, such as finding the height of a building.
Four other activities
Expand to see all activities and additional details
Show all seven activities
Collaborative Problem Solving
Show steps
Fosters collaboration and deepens understanding through peer interaction.
Show steps
-
Form study groups with classmates.
-
Select challenging trigonometry or geometry problems.
-
Work together to solve the problems, explaining your reasoning and sharing different perspectives.
Attend a Trigonometry or Geometry Workshop
Show steps
Provides an immersive learning experience with hands-on practice and expert guidance.
Browse courses on
Trigonometry
Show steps
-
Research and identify workshops that align with your learning goals.
-
Register for and attend a workshop.
-
Actively participate in the workshop's activities and discussions.
-
Apply what you learn in the workshop to your coursework.
Illustrate Conic Section Applications
Show steps
Enhances your comprehension of conic sections and their practical applications.
Browse courses on
Conic Sections
Show steps
-
Choose a real-world scenario that involves a conic section (e.g., a parabolic trajectory or an elliptical orbit).
-
Create a visual representation (e.g., a diagram, graph, or animation) to illustrate the conic section.
-
Analyze the properties of the conic section and explain how they relate to the real-world application.
Contribute to Math Stack Exchange
Show steps
Enhances your problem-solving skills and deepens your understanding of the subject matter.
Browse courses on
Trigonometry
Show steps
-
Create an account on Math Stack Exchange.
-
Browse open questions related to trigonometry or geometry.
-
Provide thoughtful and well-explained answers to questions.
-
Engage in discussions with other users to refine your understanding.
Explore Online Tutorials
Show steps
Supplements your learning with additional resources and expert guidance.
Show steps
Show steps
Show steps
- Identify reputable online platforms or educators that offer tutorials on trigonometry and geometry.
- Select tutorials that align with your learning objectives.
- Follow the tutorials, take notes, and practice the concepts.
Revisit basic geometry
Show steps
Reinforces your understanding of geometric principles and their applications.
Browse courses on
Geometry
Show steps
Show steps
Show steps
- Review the definitions and properties of basic geometric shapes, such as triangles, circles, and squares.
- Solve problems involving angles, lengths, and areas of geometric shapes.
- Identify and apply geometric concepts in real-world situations.
Trigonometric Identities Practice
Show steps
Strengthens your ability to manipulate and apply trigonometric identities.
Browse courses on
Trigonometry
Show steps
Show steps
Show steps
- Memorize fundamental trigonometric identities (e.g., sin²x + cos²x = 1).
- Practice using identities to solve trigonometric equations and simplify expressions.
- Apply trigonometric identities to real-world applications, such as finding the height of a building.
Four other activities
Expand to see all activities and additional details
Show all seven activities
Collaborative Problem Solving
Show steps
Fosters collaboration and deepens understanding through peer interaction.
Show steps
Show steps
Show steps
- Form study groups with classmates.
- Select challenging trigonometry or geometry problems.
- Work together to solve the problems, explaining your reasoning and sharing different perspectives.
Attend a Trigonometry or Geometry Workshop
Show steps
Provides an immersive learning experience with hands-on practice and expert guidance.
Browse courses on
Trigonometry
Show steps
Show steps
Show steps
- Research and identify workshops that align with your learning goals.
- Register for and attend a workshop.
- Actively participate in the workshop's activities and discussions.
- Apply what you learn in the workshop to your coursework.
Illustrate Conic Section Applications
Show steps
Enhances your comprehension of conic sections and their practical applications.
Browse courses on
Conic Sections
Show steps
Show steps
Show steps
- Choose a real-world scenario that involves a conic section (e.g., a parabolic trajectory or an elliptical orbit).
- Create a visual representation (e.g., a diagram, graph, or animation) to illustrate the conic section.
- Analyze the properties of the conic section and explain how they relate to the real-world application.
Contribute to Math Stack Exchange
Show steps
Enhances your problem-solving skills and deepens your understanding of the subject matter.
Browse courses on
Trigonometry
Show steps
Show steps
Show steps
- Create an account on Math Stack Exchange.
- Browse open questions related to trigonometry or geometry.
- Provide thoughtful and well-explained answers to questions.
- Engage in discussions with other users to refine your understanding.
Career center
Learners who complete Trigonometría y geometría analítica will develop knowledge and skills
that may be useful to these careers:
Topographer
Topographer
Topographers create maps and charts of the Earth's surface. They use trigonometry and geometry to measure and record the elevation, shape, and features of the land. This course will help you build a foundation in trigonometry and geometry, which are essential for success as a Topographer. You will learn the principles of trigonometry, the concepts of geometry, and how to apply these principles to real-world problems.
Geodetic Surveyor
Geodetic Surveyor
Geodetic Surveyors measure and map the Earth's surface. They use trigonometry and geometry to determine the location and elevation of points on the Earth's surface. This course will help you build a foundation in trigonometry and geometry, which are essential for success as a Geodetic Surveyor. You will learn the principles of trigonometry, the concepts of geometry, and how to apply these principles to real-world problems.
Surveyor
Surveyor
Surveyors measure and map the Earth's surface. They use trigonometry and geometry to determine the location and elevation of points on the Earth's surface. This course will help you build a foundation in trigonometry and geometry, which are essential for success as a Surveyor. You will learn the principles of trigonometry, the concepts of geometry, and how to apply these principles to real-world problems.
Geometrist
Geometrist
Geometrists study the properties and behavior of shapes and spatial relationships. They use trigonometry and geometry to understand and predict the behavior of the physical world. This course will help you build a foundation in trigonometry and geometry, which are essential for success as a Geometrist. You will learn the principles of trigonometry, the concepts of geometry, and how to apply these principles to real-world problems.
Cartographer
Cartographer
Cartographers create maps and charts that represent the Earth's surface. They use trigonometry and geometry to determine the location and shape of landmasses, bodies of water, and other features. This course will help you build a foundation in trigonometry and geometry, which are essential for success as a Cartographer. You will learn the principles of trigonometry, the concepts of geometry, and how to apply these principles to real-world problems.
Photogrammetrist
Photogrammetrist
Photogrammetrists use aerial photographs to create maps and charts. They use trigonometry and geometry to determine the location and shape of landmasses, bodies of water, and other features. This course will help you build a foundation in trigonometry and geometry, which are essential for success as a Photogrammetrist. You will learn the principles of trigonometry, the concepts of geometry, and how to apply these principles to real-world problems.
Architect
Architect
Architects design and build buildings and other structures. They use trigonometry and geometry to calculate the angles and distances of buildings and structures. This course will help you build a foundation in trigonometry and geometry, which are essential for success as an Architect. You will learn the principles of trigonometry, the concepts of geometry, and how to apply these principles to real-world problems.
Hydrologist
Hydrologist
Hydrologists study the movement and distribution of water on the Earth's surface and in the atmosphere. They use trigonometry and geometry to measure and analyze the flow of water in rivers, lakes, and aquifers. This course will help you build a foundation in trigonometry and geometry, which are essential for success as a Hydrologist. You will learn the principles of trigonometry, the concepts of geometry, and how to apply these principles to real-world problems.
Transportation Engineer
Transportation Engineer
Transportation Engineers design and build roads, bridges, and other transportation systems. They use trigonometry and geometry to calculate the angles and distances of roads and bridges. This course will help you build a foundation in trigonometry and geometry, which are essential for success as a Transportation Engineer. You will learn the principles of trigonometry, the concepts of geometry, and how to apply these principles to real-world problems.
Civil Engineer
Civil Engineer
Civil Engineers design and build roads, bridges, and other structures. They use trigonometry and geometry to calculate the angles and distances of roads and bridges. This course will help you build a foundation in trigonometry and geometry, which are essential for success as a Civil Engineer. You will learn the principles of trigonometry, the concepts of geometry, and how to apply these principles to real-world problems.
Oceanographer
Oceanographer
Oceanographers study the oceans and their physical, chemical, and biological properties. They use trigonometry and geometry to measure and analyze the depth, temperature, and salinity of the ocean. This course will help you build a foundation in trigonometry and geometry, which are essential for success as an Oceanographer. You will learn the principles of trigonometry, the concepts of geometry, and how to apply these principles to real-world problems.
Astronomer
Astronomer
Astronomers study the stars, planets, and other celestial objects. They use trigonometry and geometry to calculate the distances, sizes, and motions of these objects. This course will help you build a foundation in trigonometry and geometry, which are essential for success as an Astronomer. You will learn the principles of trigonometry, the concepts of geometry, and how to apply these principles to real-world problems.
Geophysicist
Geophysicist
Geophysicists study the Earth's physical properties and processes. They use trigonometry and geometry to measure and analyze the Earth's magnetic field, gravity, and seismic waves. This course will help you build a foundation in trigonometry and geometry, which are essential for success as a Geophysicist. You will learn the principles of trigonometry, the concepts of geometry, and how to apply these principles to real-world problems.
Meteorologist
Meteorologist
Meteorologists study the Earth's atmosphere and its weather patterns. They use trigonometry and geometry to measure and analyze the temperature, pressure, and humidity of the air. This course will help you build a foundation in trigonometry and geometry, which are essential for success as a Meteorologist. You will learn the principles of trigonometry, the concepts of geometry, and how to apply these principles to real-world problems.
Actuary
Actuary
Actuaries use mathematics and statistics to assess risk and uncertainty. They use trigonometry and geometry to calculate probabilities and make predictions. This course will help you build a foundation in trigonometry and geometry, which are essential for success as an Actuary. You will learn the principles of trigonometry, the concepts of geometry, and how to apply these principles to real-world problems.
For more career information including salaries, visit:
OpenCourser.com/course/nh213v/trigonometria
Reading list
We've selected 11 books
that we think will supplement your
learning. Use these to
develop background knowledge, enrich your coursework, and gain a
deeper understanding of the topics covered in
Trigonometría y geometría analítica.
Este libro de texto clásico proporciona una cobertura completa de geometría analítica, incluyendo secciones cónicas y aplicaciones. Su enfoque sistemático y riguroso lo convierte en un valioso recurso para el estudio de este tema.
Este libro ofrece una introducción integral a la trigonometría, cubriendo conceptos fundamentales, identidades y aplicaciones. Proporciona una base sólida para el estudio posterior en geometría analítica.
Este libro de texto proporciona una introducción integral a la geometría analítica. Su enfoque sistemático y sus numerosos ejemplos lo convierten en un valioso recurso para el estudio de este tema.
Este libro proporciona una comprensión profunda de los conceptos matemáticos fundamentales, incluyendo trigonometría y geometría analítica. Su enfoque práctico y sus numerosos ejemplos lo convierten en un recurso invaluable para aplicar las matemáticas en situaciones del mundo real.
Save
Este libro proporciona una comprensión profunda de los conceptos matemáticos fundamentales, incluyendo trigonometría y geometría analítica. Su enfoque práctico y sus numerosos ejemplos lo convierten en un recurso invaluable para aplicar las matemáticas en situaciones del mundo real.
Este libro proporciona una cobertura integral del álgebra universitaria y la trigonometría. Es ideal para estudiantes que buscan una comprensión profunda de estos temas.
Este libro ofrece una revisión de los conceptos matemáticos fundamentales necesarios para el cálculo, incluyendo trigonometría y geometría analítica. Es ideal para estudiantes que buscan refrescar sus conocimientos o prepararse para estudios posteriores.
Este libro proporciona una cobertura de los conceptos matemáticos fundamentales necesarios para la economía y los negocios, incluyendo trigonometría y geometría analítica. Es ideal para estudiantes que buscan aplicar las matemáticas en contextos del mundo real.
Este libro ofrece una cobertura completa de la trigonometría, desde conceptos fundamentales hasta aplicaciones avanzadas. Su enfoque claro y conciso lo convierte en una excelente opción para aprender los fundamentos de la trigonometría.
Este libro de texto integral combina el estudio del cálculo con la geometría analítica. Proporciona una base sólida para el estudio posterior en matemáticas y ciencias.
Este libro ofrece una introducción sencilla y accesible a la trigonometría. Es ideal para estudiantes que buscan comprender los conceptos fundamentales sin demasiada complejidad.
For more information about how these books relate to this course, visit:
OpenCourser.com/course/nh213v/trigonometria
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Effort
8 hrs/semana
Level
Introductory
Via
Coursera
Institution
Universidad Nacional Autónoma de México
Instructors
Mario Jiménez Velasco
Victoria Rojas López
Language
Español
Good to know
Está orientado a estudiantes que desean fortalecer sus conocimientos en trigonometría y geometría analítica
Aborda conceptos básicos de geometría analítica, ecuaciones de la recta, parábola, circunferencia y elipse
Ofrece aplicaciones prácticas de la trigonometría y la geometría analítica
Es impartido por profesores experimentados, Mario Jiménez Velasco y Victoria Rojas López
Requiere conocimientos previos de matemáticas básicas
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