- 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.

*
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:

- (d) Why more than
one angle can correspond to the same physical direction in the
plane, and how to tell whether two given angles correspond to
the same, or different, directions
*(The material in this section requires a understanding of the material in the earlier Sections (b) and (c) of this chapter. These can be reviewed by clicking on the appropriate links above.)*

**LINKS FOR CHAPTER 1 TOPICS:**

*Click on the link for the appropriate topic below for more information
on that topic. In general, it would be a good idea to go through the
material in the order listed, unless you are returning to this page
for a refresher on a particular topic (or topics).
*