Trig Equations and Applications

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How to Distinguish between Trigonometry Functions and Relations

Technically, an inverse trig function is supposed to have only one output for each input. (Part of the definition of an inverse is that the function and inverse are one-to-one.) With any one-to-one function [more…]

Identify the Domains and Ranges of Inverse Trigonometry Functions

A function that has an inverse has exactly one output (belonging to the range) for every input (belonging to the domain), and vice versa. To keep inverse trig functions consistent with this definition, [more…]

The Trigonometry Functions Table

You can use this table of values for trig functions when solving problems, sketching graphs, or doing any number of computations involving trig. The values here are all rounded to three decimal places. [more…]

How to Find Solutions for a Multiple-Angle Trigonometry Function

Multiple-angle trig functions include [more…]

Rewrite a Simple Trigonometry Equation Using an Inverse to Solve It

The simplest type of trigonometry equation is the one that you can immediately rewrite as an inverse in order to determine the solutions. Some examples of these types of equations include: [more…]

How to Solve a Trigonometry Equation by Factoring Quadratics

Quadratic equations are nice to work with because, when they don’t factor, you can solve them by using the quadratic formula. The types of quadratic trig equations that you can factor are those like tan [more…]

How to Factor Trigonometry Expressions with Degrees Higher than 2

Although factoring quadratics is a breeze, factoring trigonometry equations with higher degrees can get a bit nasty if you don’t have a nice situation such as just two terms or a quadratic-like equation [more…]

Find the Area of a Triangle Using ASA

When you have two angles in a triangle and the side between them (ASA), you can use trig to find the area of the triangle. The formulas go as follows.

In triangle [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…]

How to Measure the Distance to the Moon Using Trigonometry

One of the earliest applications of trigonometry was in measuring distances that you couldn't reach, such as distances to planets or the moon or to places on the other side of the world. Consider the following [more…]

How to Measure the Speed of a Car around a Race Track

A race car is going around a circular track. A photographer standing at the center of the track takes a picture, turns 80 degrees, and then takes another picture 10 seconds later. If the track has a diameter [more…]

How to Compare Slice Sizes on Two Pizzas Using Trigonometry

Some fraternity brothers want to order pizza — and you know how hungry college men can be. The big question is, which has bigger slices of pizza: a 12-inch pizza cut into six slices, or a 15-inch pizza [more…]

How to Find the Distance across a Pond

Trigonometry is very handy for finding distances that you can’t reach to measure. Imagine that you want to string a cable diagonally across a pond (so you can attach a bunch of fishing line and hooks). [more…]


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