Pre-Calculus All-in-One For Dummies

Chapter 9

Homing In on the Friendliest Angles

IN THIS CHAPTER

Placing triangles on the unit circle

Solving practical problems using angle values

Measuring the length of arcs

In this chapter, the trig functions described earlier in the book are taken a bit farther in their properties and uses. The most commonly found angles in examples and applications are 30°, 45°, 60°, and 90°, and their multiples. Why? Because their function values are so cooperative! Other angles occur in real life, and you can use a calculator to find the values needed, but it’s just easier to present the nicer, friendlier angles here!

Building on the Unit Circle

The unit circle is a vital part of the study of trigonometry. The angles are measured counterclockwise if the angle measure is positive, and clockwise if it is negative. You can spin around several times to create a really large or really small angle. But the nice thing is that the function values you find on the unit circle are from the coordinates of the points. The points don’t change; you just have to match the angle with the correct coordinates.

Familiarizing yourself with the most common angles

In pre-calculus, you often want function values ...