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But they also have very useful definitions using the coordinates of points on a graph. The opposite side is always that side that doesn’t help make up the angle, and the adjacent side is always one of the sides of the angle.Ĭoordinate Definitions for Trigonometry Functions The trig functions can be defined using the measures of the sides of a right triangle. But the designations of opposite and adjacent can change - depending on which angle you’re referring to at the time. The label hypotenuse always remains the same - it’s the longest side. Right Triangle Definitions for Trigonometry Functions The basic trig functions can be defined with ratios created by dividing the lengths of the sides of a right triangle in a specific order. Or about 1.4 times as long as those two legs. With the isosceles right triangle, the two legs measure the same, and the hypotenuse is always

Or about 1.7 times as big as the shortest side. When you have a 30­60­90 right triangle, the measure of the hypotenuse is always twice the measure of the shortest side, and the other leg is always What’s so special about the two right triangles shown here is that you have an even more special relationship between the measures of the sides - one that goes beyond (but still works with) the Pythagorean theorem. Special Right Triangles Every right triangle has the property that the sum of the squares of the two legs is equal to the square of the hypotenuse (the longest side). The formulas particular to trigonometry have: sin (sine), cos (cosine), and tan (tangent), although only sin is represented here. In the formulas given here, you have: r (radius); d (diameter or distance); b (base or measure of a side); h (height); a, b, c (measures of sides); x, y (coordinates on a graph); m (slope); M (midpoint); h, k (horizontal and vertical distances from the center); θ (angle theta); and s (arc length). The main trick to using formulas is to know what the different letters represent. A formula gives a relationship between particular quantities and units. A formula provides you a rule or equation that you can count on to work, every single time. But trigonometry also has some special formulas usually found just in those discussions. 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.įormulas to Help You in Trigonometry Many of the formulas used in trigonometry are also found in algebra and analytic geometry.

Get to know some special rules for angles and various other important functions, definitions, and translations.

Trigonometry For Dummies From Trigonometry For Dummies, 2nd Edition by Mary Jane Sterling Trigonometry is the study of triangles, which contain angles, of course.