Contextualization

Trigonometric equations are those that involve trigonometric functions, such as sine, cosine, and tangent, among others, and research on these equations has a long history with various applications ranging from astronomy to civil engineering. In summary, a trigonometric equation is a mathematical equation that equates a trigonometric function of a variable to a constant or another trigonometric function.

Ancient Greeks used trigonometric functions to study the relationship between the sides of a triangle, while Babylonians and Egyptians used them for astronomical purposes. Currently, the study of trigonometric equations is one of the main topics in high school and college mathematics courses.

Among the skills you will acquire with this project are: solving equations involving sine, cosine, and tangent functions, as well as developing socio-emotional skills such as time management, communication, problem-solving, and creative thinking. This project has been designed to be a challenge both individually and as a group, and we hope you will have a great learning experience with it.

To assist you in your studies, here are some reliable resources you can use:

1. Khan Academy - Trigonometry
2. SOS Mathematics - Trigonometric Equations
3. Wolfram MathWorld - Trigonometric Equations

Finally, remember that this project is not just about solving mathematical problems, but also about teamwork and time management. Value the learning process and not just the final result.

Practical Activity

Activity Title: The Construction of Sundials

Project Objective:

Learn to apply the concepts of trigonometric equations through the construction of a sundial, an ancient tool used to measure time.

Project Description:

Students will be divided into groups of 3 to 5. Each group will be responsible for building a functional sundial that will demonstrate the practical application of trigonometric equations. To do this, it will be necessary to calculate the angle of the gnomon (the object that casts the shadow) of the sundial, based on the latitude of the location where they live.

Required Materials:

1. Cardboard or other sturdy material to build the sundial disk
2. Pencil or pen for markings
3. Ruler
4. Protractor
5. Barbecue stick or other pointed object to serve as the gnomon
6. Glue
7. Common clock for time checking
8. Compass

Activity Steps:

1. Research: Students begin by investigating the latitude of their city and its correlation with the gnomon angle.
2. Calculations: Students use trigonometric equations to calculate the angle that the gnomon must have for the sundial to be accurate.
3. Sundial construction: Students draw a circle and mark the numbers of a common clock from 1 to 12. Then, they place the gnomon in the center pointing north (using the compass), with the previously calculated angle.
4. Validation: Students adjust the position of the sundial at noon (using the common clock) and make observations throughout the day to verify the accuracy of the sundial.

Project Delivery:

After completing the activity, students must prepare a report containing:

1. Introduction: contextualizing the theme, explaining the relevance of trigonometric equations in the construction of sundials and the project's objective.
2. Development: explaining the theory of trigonometric equations, describing the process of building the sundial in detail, the methodology used, and presenting the results obtained.
3. Conclusion: summarizing the main points of the work, adding the learnings obtained, describing the challenges encountered, and the proposed solutions.
4. Bibliography: indicating the sources that were used to support the project.

This practical activity interweaves theoretical knowledge with practical application, allowing students a greater understanding of the use of trigonometric equations in everyday life.