Contextualization

Introduction

Trigonometry is an area of mathematics that studies the relationships between the lengths of two sides of a right triangle, for different values of its angles. Trigonometric functions, such as sine, cosine, and tangent, are used to describe these relationships.

In the study of trigonometric functions, graphs play a fundamental role because they allow a clearer and more intuitive visualization of the periodic properties of these functions.

For example, the sine and cosine functions are periodically repeated after an interval of 2π, which can be effectively illustrated through graphs.

Contextualization

Studying the graphs of trigonometric functions not only deepens our understanding of mathematics but also has various applications in the real world.

In physics, these functions are essential for understanding phenomena such as sound waves and light, which are oscillatory and periodic phenomena, just like trigonometric functions.

Engineering, chemistry, economics, among many other areas, also employ trigonometric functions to analyze and predict periodic behaviors.

Activity

Activity Title: Designing the World with Trigonometry

Project Objective

The objective of the project is to create a virtual exhibition that relates the study of trigonometric functions and their graphs to real-world phenomena. In this way, students will be able to see how present Trigonometry is in our daily lives.

Detailed Project Description

Students, in groups of 3 to 5, must choose a periodic phenomenon (sound waves, lunar cycles, Earth's rotation, pendulum movements, tide variation, economic cycles, temperature variation during the day, among others) that can be represented by trigonometric functions.

After choosing their phenomenon, students should research and understand how trigonometry is used to represent it. Students should use the graphs of trigonometric functions to illustrate this phenomenon. It is interesting to use the GeoGebra application to create these graphs.

Students should also seek interdisciplinarity, correlating Mathematics with another relevant discipline for the chosen phenomenon (Physics, Biology, Geography, Economics, among others).

The virtual exhibition will be conducted by each group through a video presentation, which must be recorded and edited in a professional and engaging format. The video should contain the explanation of the theory and information about the chosen phenomenon.

Required Materials

• Internet access for research and use of GeoGebra.
• Camera (can be from a smartphone) for video recording.
• Video editing software (free examples: DaVinci Resolve, iMovie, Windows Movie Maker).
• Computer for video editing and report elaboration.

Step by Step

1. Form groups of 3 to 5 students.
2. Each group must choose a periodic phenomenon to study.
3. Conduct research to understand how trigonometry is used to represent the chosen phenomenon.
4. Use GeoGebra to create graphs of trigonometric functions that model the phenomenon.
5. Research the interdisciplinarity of the chosen phenomenon, that is, how it relates to other disciplines.
6. Develop a script for the video.
7. Record and edit the video.
8. Create a detailed report of the activity.

Project Deliverables and Connections with Activities

The final delivery of this project will consist of two main components: a video and a written report.

1. Video: This video should be a virtual exhibition where the group explains the theory of trigonometric functions and illustrates its application in the chosen phenomenon. This video should be between 10 and 15 minutes, be clear and didactic, and have been edited to give a professional appearance.

2. Report: To complement the video, students must prepare a report containing an introduction, development, conclusions, and bibliography.

• Introduction: In this section, students must present and contextualize the chosen theme, explain its relevance and application in the real world, and expose the project's objective.

• Development: Here, students must explain the theory of trigonometric functions, describe the activity carried out, indicate the methodology used, and the tools used, such as GeoGebra. It should show and discuss the results obtained, represented through the graphs.

• Conclusions: Students must summarize the main points of the research, explain what they have learned, and draw conclusions about the project.

• Bibliography: In this section, students must list all the research sources used throughout the project.

Therefore, students should go through an experience that, in addition to mathematics, involves competencies such as teamwork, time management, use of technology, and effective communication.