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Trigonometry

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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…]

How to Change Radians to Degrees

Many math problems require you to change measurements from radians to degrees. You often perform mathematical computations in radians, but then convert to degrees so the final answers are easier to visualize [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…]

The Cosine Function: Adjacent over Hypotenuse

When you’re using right triangles to define trigonometry functions, the trig function cosine, abbreviated cos, has input values that are angle measures and output values that you obtain from the ratio [more…]

How to Find the Trigonometry Function of an Angle in a Unit Circle

You can determine the trig functions for any angles that relate to the unit circle. To do this, you can use the rules for reference angles, the values of the functions of certain acute angles, and the [more…]

How to Determine the Vertical Distance Travelled by a Rocket

Trigonometry functions have plenty of everyday uses. You can use a trigonometry function to determine how far a projectile travels vertically over a certain period of time. [more…]

Using the Angle-Sum Identity

Three basic trigonometry identities involve the sums of angles; the functions involved in these identities are sine, cosine, and tangent. You can also adapt these three basic angle-sum identities for the [more…]

Using the Double-Angle Identity for Cosine

Identities for angles that are twice as large as one of the common angles (double angles) are used frequently in trig. These identities allow you to deal with a larger angle in the terms of a smaller and [more…]

How to Use Half-Angle Identities to Find the Sine of an Angle

By adding, subtracting, or doubling angle measures, you can find lots of exact values of trigonometry functions using the functions of angles you already know. For example, even though you can use a difference [more…]

How to Work Both Sides of a Trig Identity

With a trigonometry identity, working on both sides of the equation is even more fun than working on both sides of an algebraic equation. In algebra, you can multiply each side by the same number, square [more…]

Change to Sines and Cosines in a Trigonometry Identity

With some trig identities, you may decide to simplify matters by either changing everything to sines and cosines or by factoring out some function. Sometimes, it isn’t clear which side you should work [more…]

When to Factor a Trigonometry Identity

You’ll know that you need to factor a trig identity when powers of a particular function or repeats of that same function are in all the terms on one side of the identity. [more…]

Break Up or Combine Fractions to Solve a Trigonometry Identity

A trig identity with fractions can work to your advantage; you’re given a plan of attack. You can work toward getting rid of the fraction and, in the process, solve the problem. Two of the main techniques [more…]

How to Remove a Third Angle to Solve a Trigonometry Identity

Sum and difference identities usually involve two different angles and then a third combined angle. When proving these trig identities, you often need to get rid of that third angle. The following example [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…]

Comparing Cosine and Sine Functions in a Graph

The relationship between the cosine and sine graphs is that the cosine is the same as the sine — only it’s shifted to the left by 90 degrees, or π/2. The trigonometry equation that represents this relationship [more…]

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