Trigonometry and Single Phase AC Generation for Electricians (Flinn)

To understand electrical theory, it is important to have a grasp of trigonometry. Whether we are talking about single phase or polyphase power, trigonometry is a key concept. This textbook, divided into three sections, provides easy-to-understand and enjoyable lessons on trigonometry, vectors and AC generation for those training and working as electricians.

Trigonometry To have a good grasp of electrical theory it is important to have a grasp of trigonometry. Whether we are talking about single phase or polyphase power, trigonometry is a key concept. The first part of this textbook will look at one of the most basic parts of trigonometry: the triangle.

What’s the deal with angles anyway?

Before we even get into trigonometry, we need to discuss angles. Don’t worry. Things are not going to get too crazy. I promise. Let’s go over the basics first. Degree. One-three-hundred-and-sixtieth of the circumference of a circle. It is also the unit by which we measure angles.

Why triangles are important

Learning about electrical theory necessitates the study of triangles. More specifically: right triangles. Before we dig too much into the right triangle, let’s go over two key points about triangles.

• All triangles have three sides. (File this fact under the “thank you Captain Obvious” category.)
• All triangles contain 180 degrees.

Pythagoras

Who is this Pythagoras and why does he matter?

Pythagoras was a Greek philosopher who lived around 500 BC. He is credited as being a philosopher and mathematician. Much of what we know of Pythagoras is from writings that were copied down hundreds of years after his death, so the validity of what we do know is questionable. He is credited with Pythagoras’ theorem when actually it has been proven that Babylonians and Indians were using variations of it for hundreds of years before he even came along. More can be found about him in this article.

Thanks for the history lesson, but get on with it!

The Pythagorean theorem, also known as Pythagoras’ theorem, is a relation in Euclidean geometry among the three sides of a right triangle. ‘It states that the square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides.

What is this big fancy word, trigonometry?

Trigonometry is the study of the relationship that exists between the sides and the angles of a triangle.

That sounds complicated and scary.

It can be, but lucky for us we are only dealing with right triangles. This makes it very simple and almost fun. (Nerd alert!)

First steps

We have already learned how to determine the sides of a triangle using the Pythagoras’ theorem. Next up is using those sides to determine the angles. Lucky for us we know that in a right triangle we already have one 90-degree angle. We also know that if we can solve any of the other two angles, the third one is easy. (All triangles have 180 degrees.) Our next step is to name the sides of the triangle. The names of these sides are dependent on something called the designate angle or theta. Theta is an angle that you determine or is determined for you.