Trigonometry and Single Phase AC Generation for Electricians

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.

Different triangles

The right triangle is the most common triangle that will be used in electrical theory. It is a good idea to have a basic understanding of other triangles as well. Here are some common triangles you will come across in trigonometry.

So what about these right triangles you were talking about?

A right triangle is a triangle that has one right angle (equal to 90 degrees). This means that the other two angles are complementary, that is, they must add to 90 degrees.

Ok, so what does a right triangle have to do with electrical?

Quite a bit actually.

In the world of electrical theory, we will have to add up values. We call these units vectors (more on the concept of vectors in a later chapter). These vectors each head in a different direction. In fact, they are 90 degrees to each other. When we add them, the sum of these two vectors ends up being the point between the two sides.

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. You can read more about Pythagoras in this article.

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.

Now once you have figured out which angle is your theta, we can get to business naming the sides.

Adjacent. This is the side that sits adjacent to the designate angle.

Opposite. This is the side that sits opposite to the designate angle.

Hypotenuse. This is the side that sits opposite the 90-degree angle.

The hypotenuse is always the longest side of the triangle and doesn’t care where the designate angle is. It only cares that it is opposite the 90-degree angle.