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Trigonometry

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Graph the Asymptote of a Tangent Function

An asymptote is a line that helps give direction to a graph of a trigonometry function. This line isn’t part of the function’s graph; rather, it helps determine the shape of the curve by showing where [more…]

Graph the Asymptotes of a Cotangent Function

The graphs of the tangent function lay the groundwork for the graphs of the cotangent function. After all, the tangent and cotangent are cofunctions and reciprocals, and have all sorts of connections. [more…]

How to Find the Area of a Triangle with SAS

When you know the lengths of two of a triangle’s sides plus the measure of the angle between those sides (SAS), you can find the area of the triangle. This method requires a little trigonometry — you have [more…]

Find Opposite-Angle Trigonometry Identities

The opposite-angle identities change trigonometry functions of negative angles to functions of positive angles. Negative angles are great for describing a situation, but they aren’t really handy when it [more…]

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. The label hypotenuse [more…]

Coordinate Definitions for Trigonometry Functions

The trig functions can be defined using the measures of the sides of a right triangle. But they also have very useful definitions using the coordinates of points on a graph. First, let let the vertex of [more…]

Signs of Trigonometry Functions in Quadrants

An angle is in standard position when its vertex is at the origin, its initial side is on the positive x-axis, and the terminal side rotates counterclockwise from the initial side. The position of the [more…]

Laws of Sines and Cosines

The laws of sines and cosines give you relationships between the lengths of the sides and the trig functions of the angles. These laws are used when you don’t have a right triangle — they work in any triangle [more…]

Exact Trigonometry Functions for Selected Acute Angles

Using the lengths of the sides of the two special right triangles — the 30-60-90 right triangle and the 45-45-90 right triangle — the following exact values for trig functions are found. Using these values [more…]

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 Pythagorean theorem is written: [more…]

Finding Values for Trigonometry Functions

You probably know many of the trigonometry functions for the more common angles. Some favorites are: [more…]

Identifying Algebraic Properties Most Often Used When Solving Identities

Solving identities is almost a rite of passage for those studying trigonometry. Tackling the prospect of solving identities — and later simplifying trig expressions in calculus — goes much more smoothly [more…]

10 Ways to Compute Trigonometry Functions without Trig Functions

A trigonometric function has input values that are angles and output values that are real numbers. You have two choices when inputting values into a trig function: You can use degrees or radians. Most [more…]

The Polar Coordinate System

The most familiar graphing plane is the one using the Cartesian coordinates. You find two perpendicular lines called axes.The horizontal axis (or x-axis) and vertical axis [more…]

Without Geometry There Would Be No Trigonometry

Trigonometry is a subject that has to be studied after some background in geometry. Why? Because trigonometry has its whole basis in triangles and angle measures and circles. Geometric studies acquaint [more…]

Formulas to Help You in Trigonometry

Many of the formulas used in trigonometry are also found in algebra and analytic geometry. But trigonometry also has some special formulas usually found just in those discussions. A formula provides you [more…]

Degree/Radian Equivalences for Selected Angles

As you study trigonometry, you'll find occasions when you need to change degrees to radians, or vice versa. A formula for changing from degrees to radians or radians to degrees is: [more…]

Trigonometry For Dummies Cheat Sheet

Trigonometry is the study of triangles, which contain angles, of course. Get to know some special rules for angles and various other important functions, definitions, and translations. Sines and cosines [more…]

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