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.
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1.1: Angles
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Before we even get into trigonometry, we need to discuss angles.
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1.2: Triangles
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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 and All triangles contain 180 degrees.
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1.3: Pythagoras
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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.
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1.4: Naming Right Triangle Sides
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Trigonometry is the study of the relationship that exists between the sides and the angles of a triangle.
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1.5: Trigonometry Functions
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When determining the designate angle we can use different ratios of sides: (1) We can use a ratio of the opposite to the hypotenuse. (2) We can use a ratio of the adjacent to the hypotenuse. (3) We can use a ration of the opposite to the adjacent.
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1.6: Power and Impedance Triangles
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When dealing with DC circuits the only thing that opposes current is the resistance in the circuit. As we will learn in later units, AC adds a component that opposes current as well. This is called reactance and it runs 90 degrees to the circuit resistance. This means it is not possible to add them together arithmetically; it has to be done using the Pythagoras’ theorem. When you add these two together, you get a total opposition to current flow called impedance.