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Trig Basics

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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. [more…]

How to Find the Midpoint of a Line Segment

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

How to Pinpoint the Center of a Triangle

To find the center of a triangle, all you need are the locations of the three corners and the midpoints of the sides opposite those vertices. (It’s also a good idea to draw the triangle to help you see [more…]

How to Recognize Parallel and Perpendicular Lines

There’s an easy way to tell whether two lines are parallel or perpendicular to each other in a graph — if you can determine the coordinates of some points on the lines: the lines are [more…]

How to Use Function Notation

Function notation is like shorthand writing: if you understand it, you’ll save a lot of time (and pencil lead) when working out a problem. Without notation, defining a function or explaining how it works [more…]

Determine Domain and Range in a Trig Function

When using functions, you can think of a domain as all the possible values you can put in for the input variable, and a range as all the possible values that you get back after performing the operations [more…]

How to Find an Inverse Trig Function

Not all functions have inverses, and not all inverses are easy to determine. Here are some useful methods for finding inverses of basic algebraic functions. [more…]

The Most Frequently Used Trig Angles

There are certain angles that you will use frequently when you work with trigonometry functions. You can find these angles by cutting a graph into four parts, and then dividing those parts into smaller [more…]

Graph Angles in a Standard Position

In trigonometry and most other math topics, you draw angles in a standard, universal position, so that mathematicians around the world are drawing and talking about the same thing. [more…]

Identify Coterminal Angles

An angle in standard position on the coordinate plane has its vertex at the origin and its initial (beginning) side along the positive x-axis. An angle’s [more…]

How to Rename Coterminal Angles

Any angle can have many, many descriptions in terms of angle measures, because an angle measure is equivalent to the measures of its coterminal angles. The most frequently used positive angle measures [more…]

Define a Right Triangle and Its Parts

If you’re looking at their angles, triangles can be right, acute, or obtuse. So what makes a triangle right? Quite simply, a right triangle has a right angle in it. But it can only have one right angle [more…]

How to Solve for a Missing Right Triangle Length

One of the nice qualities of right triangles is that you can use trigonometry to find the length of one side if you know the lengths of the other two sides. You don’t have this luxury with just any triangle [more…]

Using Isosceles Right Triangles

The isosceles right triangle, or the 45-45-90 right triangle, has some special properties. For example, the two acute angles are equal, making the lengths of the two legs opposite them equal, too. What’s [more…]

Identify Common Pythagorean Triples

A Pythagorean triple is a list of three numbers that fits the Pythagorean theorem — the square of the largest number is equal to the sum of the squares of the two smaller numbers. The multiple of any Pythagorean [more…]

How to Change Degrees to Radians

Many math problems require you to change measurements from degrees to radians. Degree measures are more familiar than radians to most people. A circle is divided into 360 [more…]

How to Use Radians to Solve a Trig Problem

Using radians is very helpful when you are doing trigonometry applications involving the length of an arc of a circle, which is part of its circumference. This might include measuring the sweep of a hand [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 Divide a Line Segment into Multiple Parts

If you can find the midpoint of a segment, then 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 [more…]

How to Locate the Center of a Circle

You can use algebra to find the center of a circle. If the endpoints of one diameter of a circle are (x1,y1) and (x2,y2), then the center of the circle has the following coordinates: [more…]

Using the 30-60-90 Right Triangle

A 30-60-90 right triangle has angles measuring just what the name says. The two acute, complementary angles are 30 and 60 degrees. These triangles are great to work with, because the angle measures, all [more…]

Transforming the Graphs of Trigonometry Functions

The graphs of the trigonometric functions can take on many variations in their shapes and sizes. Starting from the general form, you can apply transformations by changing the amplitude , or the period [more…]

Understanding Trigonometry Terms

Like any math or science topic, trigonometry has its own unique vocabulary. Trigonometry uses functions with names like sine, cosine, and secant, and Greek letters like alpha and beta to represent common [more…]

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

When you translate a trig function to solve a problem, you can think of the translation as a slide. This means that the function has the same shape graphically, but the graph of the function slides up, [more…]

Reflecting Functions Vertically or Horizontally

Two types of trigonometry transformations act like reflections or flips that you see in graphing or geometry. One transformation changes all positive outputs to negative and all negative outputs to positive [more…]

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