Chapter 10: Foundations of Trigonometry

This section begins our study of Trigonometry and to get started, we recall some basic definitions from Geometry. A ray is usually described as a `half-line' and can be thought of as a line segment in which one of the two endpoints is pushed off infinitely distant from the other, as pictured below. The point from which the ray originates is called the initial point of the ray.

When two rays share a common initial point they form an angle and the common initial point is called the vertex of the angle. Two examples of what are commonly thought of as angles are

$$\mathrm{\backslash XYZfig}2$$

However, the two figures below also depict angles - albeit these are, in some sense, extreme cases. In the first case, the two rays are directly opposite each other forming what is known as a straight angle; in the second, the rays are identical so the `angle' is indistinguishable from the ray itself.

$$\mathrm{\backslash XYZfig}4$$