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Trig Equations and Applications

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Use the Law of Tangents with SAS

You can use the law of tangents to solve for the measures of missing parts of a triangle when you have two sides of a triangle and the angle between them [more…]

How to Find the Area of a Triangle for SSS Using Heron’s Formula

You can use Heron’s Formula to find the area of the triangle, even if you only know the sides of the triangle and not any of the angles (which is called SSS, or side-side-side, in trigonometry terms). [more…]

How to Compare Slice Sizes on Two Pizzas Using Trigonometry

You can use trigonometry to measure different parts of a circle. For example, say you want to order pizza, but you’re not sure which size to get. You need to know which pizza has bigger slices: a 12-inch [more…]

How to Find the Inverse of a Trig Function

You use inverse trigonometry functions to solve equations such as sin x = 1/2, sec x = –2, or tan 2x = 1. In typical algebra equations, you can solve for the value of [more…]

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…]


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