Tangent and Cotangent Identities | Trig Identities Cheat Sheet
Sines and cosines are two trig functions that factor heavily into any study of trigonometry they have their own formulas and rules that you’ll want to understand if you plan to study trig for very long.ĭefinition of the trig functions Right Triangle Definition Unit Circle Definition Get to know some special rules for angles and various other important functions, definitions, and translations. Therefore, you will use Trig Ratios, the Triangle Sum Theorem, and/or the Pythagorean Theorem to find any missing angle or side length measures.Trig Cheat Sheet: Trigonometry is the study of triangles, which contain angles, of course. Q: What does it mean to solve a right triangle? A: When you solve a right triangle, or any triangle for that matter, it means you need to find all missing sides and angles.
Q: Where is the adjacent side of a triangle? A: The adjacent side of a triangle is the side (leg) that is touching the angle but is not the hypotenuse. Q: Where is the hypotenuse of a right triangle? A: They hypotenuse of a right triangle is always opposite the 90 degree angle, and is the longest side. Q: When to use sohcahtoa? A: When you are given a right triangle, where two of the side lengths are given and you are asked to find the third side. We have other methods we’ll learn about in Math Analysis and Trigonometry such as the laws of sines and cosines to handle those cases. If we have an oblique triangle, then we can’t assume these trig ratios will work. Q: Is sohcahtoa only for right triangles? A: Yes, it only applies to right triangles. So how do we remember these three trig ratios and use them to solve for missing sides and angles?įinding Sides and Angles Using Inverse Trig Common Questions Remember the three basic ratios are called Sine, Cosine, and Tangent, and they represent the foundational Trigonometric Ratios, after the Greek word for triangle measurement.Īnd these trigonometric ratios allow us to find missing sides of a right triangle, as well as missing angles. Key Point: Regardless of the size of the triangle, these trigonometric ratios will always hold true for right triangles. Therefore, the sets of ratios depend only on the measure of the acute angle, not the size of the triangle. It stated that the ratios of the lengths of two sides of similar right triangles are equal.
We’ll dive further into the theory behind it in the video below, but essentially it’s taken from the AA Similarity Postulate that we learned about previously. It’s a mnemonic device to help you remember the three basic trig ratios used to solve for missing sides and angles in a right triangle.
It’s probably one of the most famous math mnemonics alongside PEMDAS.Īnd it’s an essential technique for your mathematical toolbelt. Jenn, Founder Calcworkshop ®, 15+ Years Experience (Licensed & Certified Teacher)
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