Trigonometry Worksheet printable pdf download

Chapter 7: Trigonometry

Trigonometry is the study of angles and how they can be used as a means of indirect measurement, that

is, the measurement of a distance where it is not practical or even possible to measure it directly. For

example, surveyors use trigonometry to measure the heights of mountains and distances across bodies

of water, while engineers and architects use trigonometry to ensure their buildings are being built to

exact specifications. Also, any phenomena that repeats itself on a periodic basis—the seasons,

fluctuations in sales, heartbeats—can be modeled by trigonometric functions.

Section 7.1: Introduction to Trigonometry

Angles and Quadrants

We start with a discussion of angles.

A ray is placed with its endpoint at the origin of an xy-axis system, with the ray itself lying along the

positive x-axis. The ray is allowed to rotate. Counterclockwise rotations are considered positive, and

clockwise rotations are called negative (See Fig 1).

The xy-axis system itself is subdivided into four quadrants, each defined by the x- and y-axes. These

quadrants are numbered 1 through 4, with Quadrant 1 being at the top right (where both x and y are

positive) and Quadrants 2, 3 and 4 following consecutively as the ray makes one complete rotation

around the plane (See Fig 2).

The words angle and rotation are synonymous with one another. An angle is measured from the ray’s

starting position along the positive x-axis (called its initial side) and ending at its terminal side.

Angle Relationships and Degree Measurement

Degree measurement is based on a circle, which is 360 degrees, or 360°. If a ray is allowed to rotate one

complete revolution counterclockwise around the xy-plane, starting and ending at the positive x-axis, we

say that the ray has rotated 360 degrees. Its angle measurement would be written 360°.

Smaller (or larger) rotations can then be defined proportionally. For example, if the ray rotates half-way

around the plane in the counterclockwise direction, from the positive x-axis to the negative x-axis, we

say that the ray rotated 180 degrees (half of 360 degrees), and that its angle measurement is 180°.

Similarly, if the ray rotates from the positive x-axis to the positive y-axis in a counterclockwise direction,

its rotation is 90 degrees and its angle measurement is 90°.

Trigonometry Worksheet