Trig Basics

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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…]

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…]

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…]

Identify Coterminal Angles

Two angles are coterminal if they have the same terminal side. You have an infinite number of ways to give an angle measure for a particular terminal ray. Sometimes, using a negative angle rather than [more…]

How to Rename Coterminal Angles

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

How to Change Degrees to Radians

The computation required for changing degrees to radians isn't difficult. The computation involves a few tricks, though, and the format is important. You don't usually write the radian measures with decimal [more…]

How to Change Radians to Degrees

You use the same basic proportion to change radians to degrees as you do for changing degrees to radians. The computation required for changing radians to degrees isn't difficult. For example, to change [more…]

How to Relate Radians to Radar Scans

The biggest advantage of using radians instead of degrees is that a radian is directly tied to a length — the length or distance around a circle, which is called its [more…]

Define a Right Triangle and Its Parts

A right triangle has a right angle in it. But it can only have one right angle, because the total number of degrees in a triangle is 180. If it had two right angles, then those two angles would take up [more…]

Identify Common Pythagorean Triples

A Pythagorean triple is a list of three numbers that works in 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 [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…]

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