Trigonometry

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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…]

Defining Trig Functions

Every triangle has six parts: three sides and three angles. If you measure the sides and then pair up those measurements (taking two at a time), you have three different pairings. Do division problems [more…]

How to Recognize Basic Trig Graphs

The graphs of the trig functions have many similarities and many differences. The graphs of the sine and cosine look very much alike, as do the tangent and cotangent, and then the secant and cosecant have [more…]

How to Find the Midpoint of a Line Segment

The middle of a line segment is its midpoint. To find the midpoint of a line segment, you just calculate the averages of the coordinates — easy as pie. [more…]

How to Locate the Center of a Circle

One way to describe the middle of a circle is to identify the centroid. This middle-point is the center of gravity, where you could balance the triangle and spin it around [more…]

How to Divide a Line Segment into Multiple Parts

If you can find the midpoint of a segment, you can divide it into two equal parts. Finding the middle of each of the two equal parts allows you to find the points needed to divide the entire segment into [more…]

How to Pinpoint the Center of a Triangle

If you draw lines from each corner (or vertex) of a triangle to the midpoint of the opposite sides, then those three lines meet at a center, or centroid, [more…]

How to Circumscribe a Triangle

Every triangle can be circumscribed by a circle, meaning that one circle — and only one — goes through all three vertices (corners) of any triangle. In laymen's terms, any triangle can fit into some circle [more…]

How to Recognize Parallel and Perpendicular Lines

Two lines are parallel if they have the same slope. Two lines are perpendicular if their slopes are negative reciprocals of one another. Numbers that are [more…]

How to Use Function Notation

Defining a function or explaining how it works can involve a lot of words and can get rather lengthy and awkward. Imagine having to write, "Square the input, multiply that result by 2, and then subtract [more…]

Determine Domain and Range in a Trig Function

A function consists of a rule that you apply to the input values. The result is a single output value. You can usually use a huge number of input values, and they're all part of the [more…]

How to Find an Inverse Trig Function

The trig functions all have inverses, but only under special conditions — you have to restrict the domain values. Not all functions have inverses, and not all inverses are easy to determine. Here's a nice [more…]

Translate a Trigonometry Function Up, Down, Left, or Right

A translation is a slide, which means that the function has the same shape graphically, but the graph of the function slides up or down or slides left or right to a different position on the coordinate [more…]

Reflecting Functions Vertically or Horizontally

Two types of transformations act like reflections or flips. One transformation changes all positive outputs to negative and all negative outputs to positive. The other reverses the inputs — positive to [more…]

What's a Degree in Trigonometry?

What's a degree? In trigonometry, a degree is a tiny slice of a circle. Imagine a pizza cut into 360 equal pieces (what a mess). Each little slice represents one degree. [more…]

Graph Angles in a Standard Position

Navigators, surveyors, and carpenters all use the same angle measures, but the angles start out in different positions or places. In trigonometry and most other mathematical disciplines, you draw angles [more…]

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