Trigonometry is the study of triangles and the component pieces that form triangles: angles and sides. In this chapter, you will concern yourself with the former, exploring the construction of angles and the units of measurement that assign values to angles. Specific attention is given to angles in standard position, as the coordinate plane is an essential tool in the study of trigonometry. Finally, you will calculate the lengths of arcs based upon the angles that form them.
Welcome to trigonometry, an entire course dedicated to studying one shape: the triangle. If you thought you knew something about triangles before, well, you had no idea how much you didn’t know about them. For the next 18 chapters, you and triangles are stuck on a desert island together, so you may as well start getting to know one another.
What is a triangle? It’s a two-dimensional shape formed by three line segments. Specifically, each line segment intersects the other two segments only at their endpoints. A point of intersection is called a vertex (the plural is vertices), and two intersecting sides form an angle. In this chapter, you learn how to measure an angle using degrees or radians (or rotations, if you are feeling sassy), and how to convert between degrees and radians.
The big takeaway from this chapter is understanding what radians are, because you’ll be using them a lot.