Cheat Sheet
Trigonometry For Dummies
Trigonometry is the study of triangles. Get to know some special rules for angles and some other important functions, definitions, and translations. Sines and cosines factor heavily into trigonometry and have their own formulas and rules that you'll want to understand, if you plan to study trig for long.
Special Right Triangles for Trigonometry
Trigonometry is focused on studying triangles, and some right triangles are special even in trig. The following figures show the 30-60-90 triangle and the Isosceles triangle for your trigonometry enjoyment:
Right Triangle Definitions for Trigonometry Functions
Defining the hypotenuse and the adjacent and opposite sides of triangles is what trigonometry is all about. But trig has a set of definitions for right triangles, which are shown with the following figure of a right triangle:
Trigonometry Functions for Acute Angles
Trigonometry deals with triangles, which necessarily means dealing with acute angles — those 90 degrees or less. The following table shows the exact sine, cosine, and tangent functions for select acute angles:
Degree/Radian Equivalences for Trigonometry
Radians, as units of plane angles, can be translated into degrees. If you’re using trigonometry, knowing those equivalences comes in very handy. The following table shows select equivalences:
Coordinate Definitions for Trigonometry Functions
In trigonometry, you can get up to all sorts of plots — as long as you’re plotting triangles. The coordinate definitions for each of the trig functions are shown in the following list:
Signs of Trigonometry Functions in Quadrants
When you plot triangles in trigonometry, trig functions have different signs, depending on the quadrant they’re in. In quadrant I, for example, all functions are positive. The following figure shows which functions are positive in each quadrant:
Trigonometry Formulas Worth Knowing
Trigonometry is no slouch when it comes to useful formulas. Whether you want to figure the length of an arc or the area of a triangle, the formulas in the following list can help you out:
Trigonometry Laws of Sines and Cosines
Trigonometry is the happy home of sines and cosines. However, those sines and cosines are ruled by mathematical laws. The laws for both are shown in the following lists:
