Introduction to Angles
Trigonometry is the study of angles and relationships between them. Especially important in trigonometry are the angles of a triangle. For this reason, trigonometry is closely linked with geometry. One of the major differences between trigonometry and geometry, though, is that trigonometry concerns itself with actual measurements of angles and sides of a triangle, whereas geometry focuses on establishing relationships between unmeasured angles and sides. To begin our study of trigonometry, we'll review the definition and some characteristics of angles to make sure we have a solid foundation for learning more about them.
Angles, by definition, lie in a plane, so trigonometry is a two-dimensional field of study. It will be convenient, and eventually necessary, to become familiar with the coordinate plane, which is a system of measuring and plotting points in two dimensions. The location of any point in a plane, then, can be specified by exact coordinates. A point can also be specified by a vector. A vector is like a line segment lying in a specific position--it has length and direction. Vectors can be used to determine the location of points, as well as the measure of certain angles. These basic concepts will provide a foundation for understanding the principles of trigonometry.