Skip to main content

1: 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.

• 1.1: Angles
Before we even get into trigonometry, we need to discuss angles.
• 1.2: Triangles
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.
• 1.3: Pythagoras
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.
• 1.4: Naming Right Triangle Sides
Trigonometry is the study of the relationship that exists between the sides and the angles of a triangle.
• 1.5: Trigonometry Functions
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.
• 1.6: Power and Impedance Triangles
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.
{"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9369613528251648, "perplexity": 512.5927282686071}, "config": {"markdown_headings": false, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": false}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-09/segments/1550247493803.26/warc/CC-MAIN-20190219223509-20190220005509-00422.warc.gz"}