Unit 2: Geometry in Depth
Section C: Introduction to Trigonometry
Welcome
Welcome to Section C: Introduction to Trigonometry! In this section, you’ll begin your exploration of trigonometry, a branch of mathematics that deals with the relationships between the angles and sides of triangles.
Imagine
Imagine you’re a surveyor measuring the height of a mountain or a bridge builder calculating the length of a support cable. Trigonometry provides the tools to solve these kinds of problems with precision.
Context
Previously, you’ve studied geometry and its principles. Now, we’ll extend those ideas to trigonometry, where you’ll explore the relationships between angles and sides in triangles and apply them to real-world problems.
Overview
This section covers the basic definitions of sine, cosine, and tangent, solving right triangles, understanding trigonometric ratios, and applying the Law of Sines and Cosines to various problems.
Objectives
- Understand the basic concepts of trigonometry, including sine, cosine, and tangent.
- Solve right triangles using trigonometric ratios and understand their applications.
- Explore the relationships between angles and sides in triangles using the Law of Sines and Cosines.
- Apply trigonometric concepts to real-world problems, such as surveying, engineering, and physics.
- Develop a strong foundation for more advanced topics in trigonometry.
Preparatory Guidance
Definitions and Pronunciations
- Trigonometry: The branch of mathematics that studies the relationships between the angles and sides of triangles.
- Sine: A trigonometric function that relates the opposite side of a right triangle to its hypotenuse, denoted as
.
- Cosine: A trigonometric function that relates the adjacent side of a right triangle to its hypotenuse, denoted as
.
Verbal Reading of Equations
- For
, say “sine of theta equals opposite over hypotenuse.”
- For
, say “cosine of theta equals adjacent over hypotenuse.”
Problem-Solving Strategies
- Understand and apply the basic trigonometric functions: sine, cosine, and tangent, to solve problems involving right triangles.
- Solve right triangles by applying trigonometric ratios to find unknown angles and sides.
- Explore the relationships between angles and sides in triangles using the Law of Sines and Cosines.
- Apply trigonometric concepts to real-world problems, such as surveying, engineering, and physics.
- Develop a strong foundation for more advanced topics in trigonometry, preparing you for future studies.
Considerations
How does trigonometry apply to real-world problems? Why is it important to understand the relationships between angles and sides in triangles? In what ways can you use trigonometry in your daily life or future career?