**Definition:**
Trigonometry is the branch of mathematics that studies the relationships between the angles and sides of triangles, especially right triangles.

**Key ideas:**
- Trigonometric functions (sine, cosine, tangent) relate angles to side lengths.
- The Pythagorean theorem connects the sides of a right triangle.
- Trigonometry is used to solve problems in physics, engineering, and architecture.
- It helps in understanding periodic phenomena, like waves and oscillations.

**Why this topic matters in this category:**
Trigonometry is essential for students in mathematics and science, as it provides tools for solving real-world problems involving angles and distances.