Trigonometry For Dummies

Mary Jane Sterling

• Publisher: For Dummies
• Year: 2014
• ISBN:
  9781118827574
• Edition: 2
• Topic: Mathematics
• Subtopic: Trigonometry
• Index: Mathematics

A plain-English guide to the basics of trig

Trigonometry deals with the relationship between the sides and angles of triangles... mostly right triangles. In practical use, trigonometry is a friend to astronomers who use triangulation to measure the distance between stars. Trig also has applications in fields as broad as financial analysis, music theory, biology, medical imaging, cryptology, game development, and seismology.

From sines and cosines to logarithms, conic sections, and polynomials, this friendly guide takes the torture out of trigonometry, explaining basic concepts in plain English and offering lots of easy-to-grasp example problems. It also explains the "why" of trigonometry, using real-world examples that illustrate the value of trigonometry in a variety of careers.

• Tracks to a typical Trigonometry course at the high school or college level
• Packed with example trig problems
• From the author of Trigonometry Workbook For Dummies

Trigonometry For Dummies is for any student who needs an introduction to, or better understanding of, high-school to college-level trigonometry.

Part I

Getting Started with Trigonometry

For Dummies can help you get started with lots of subjects. Visit www.dummies.com to learn more and do more with For Dummies.

In this part…

• Become acquainted with angle measures and how they relate to trig functions.
• Discover formulas that provide lengths of segments, midpoints, and slopes of lines.
• Become familiar with circles and the relationships between radii, diameters, centers, and arcs.
• Relate infinitely many angle measures to just one reference angle.
• Find a simple conversion method for changing from degrees to radians and vice versa.
• Observe the properties of special right triangles, and use the Pythagorean theorem to formulate the relationships between the sides of these right triangles.

Chapter 1

Trouncing Trig Technicalities

In This Chapter

Understanding what trigonometry is

Speaking the language by defining the words

Writing trig functions as equations

Graphing for understanding

How did Columbus find his way across the Atlantic Ocean? How did the Egyptians build the pyramids? How did early astronomers measure the distance to the moon? No, Columbus didn't follow a yellow brick road. No, the Egyptians didn't have LEGO instructions. And, no, there isn't a tape measure long enough to get to the moon. The common answer to all these questions is trigonometry.

Trigonometry is the study of angles and triangles and the wonderful things about them and that you can do with them. For centuries, humans have been able to measure distances that they can't reach because of the power of this mathematical subject.

Taking Trig for a Ride: What Trig Is

“What's your angle?” That question isn't a come-on such as “What's your astrological sign?” In trigonometry, you measure angles in both degrees and radians. You can shove the angles into triangles and circles and make them do special things. Actually, angles drive trigonometry. Sure, you have to consider algebra and other math to make it all work. But you can't have trigonometry without angles. Put an angle into a trig function, and out pops a special, unique number. What do you do with that number? Read on, because that's what trig is all about.

Sizing up the basic figures

Segments, rays, and lines are some of the basic forms found in geometry, and they're almost as important in trigonometry. As I explain in the following sections, you use those segments, rays, and lines to form angles.

Drawing segments, rays, and lines

A segment is a straight figure drawn between two endpoints. You usually name it by its endpoints, which you indicate by capital letters. Sometimes, a single letter names a segment. For example, in a triangle, a lowercase letter may refer to a segment opposite the angle labeled with the corresponding uppercase letter.

A ray is another straight figure that has an endpoint on one end, and then it just keeps going forever in some specified direction. You name rays by their endpoint first and then by any other point that lies on the ray.

A line is a straight figure that goes forever and ever in either direction. You only need two points to determine a particular line — and only one line can go through both of those points. You can name a line by any two points that lie on it.

Figure 1-1 shows a segment, ray, and line and the different ways you can name them using points.

Figure 1-1: Segment AB, ray CD, and line EF.

Intersecting lines

When two lines intersect — if they do intersect — they can only do so at one point. They can't double back and cross one another again. And some curious things happen when two lines intersect. The angles that form between those two lines are related to one another. Any two angles that are next to one another and share a side are called adjacent angles. In Figure 1-2, you see several sets of intersecting lines and marked angles. The top two figures indicate two pairs of adjacent angles. Can you spot the other two pairs? The angles that are opposite one another when two lines intersect also have a special name. Mathematicians call these angles vertical angles. They don't have a side in common. You can find two ...