# KIM MALTMAN'S MINI-COURSE ON TRIG BASICS

## CHAPTER 1:THE BASICS OF ANGLES AND ANGULAR MEASURE

OVERVIEW:

A crucial concept basic to the study of trigonometry is the idea of an "angle". Without a good understanding of the basic geometrical meaning of angles and angular measure, developing a good understanding of trigonometry is essentially impossible. In this chapter, in order to provide a review of this topic for students who may benefit from such a review, we discuss the basic ideas of angles and angular measure, and review the common units (degrees or radians) used to specify angles, i.e. directions in the plane. We also explain why it is that the same physical direction in the plane can correspond to more than one value of the angle describing it.

We begin by providing some physical motivation for why we might want to specify directions in the plane using numbers (angles) in the first place, and then discuss the basic conventions that allow us to do any of the following:

• Given a physical direction in the plane, to correctly determine the angle(s) (in radians or degrees) to which this direction corresponds.

• Given an angle (in degrees or radians), to determine the correct direction in the plane to which this angle corresponds.

• Given an angle in degrees, how to re-express it in radians.

• Given an angle in radians, how to re-express it in degrees.

• Given two different angles, how to determine whether they correspond to the same, or to different, physical directions in the plane.

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