Angles and the trigonometric functions

This chapter starts with angles and the two ways to measure them: degrees and radians. It then defines the six trigonometric functions, first for the angles of a right triangle and then for any angle at all.

Every later chapter builds on these ideas, so take your time with the examples.

This chapter covers the following topics:

Angles and their measure

Angles in standard position, degrees, coterminal angles, radians, arc length, the area of a sector, and angular speed.

Right triangle trigonometry

The six trigonometric functions as ratios of sides, the special 30°-60°-90° and 45°-45°-90° triangles, and cofunctions.

Trigonometric functions of any angle

The trigonometric functions of angles in every quadrant, their signs, reference angles, and the basic identities.

The unit circle

The trigonometric functions of real numbers, values on the unit circle, and even and odd properties.

Solving right triangles

Finding the missing sides and angles of a right triangle, angles of elevation and depression, and bearings.

Practice questions

Practice problems on every section of this chapter, with full step-by-step solutions.