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### The Origin of the Half-Angle Identities for Sine

The trig identities come in sums, differences, ratios, multiples, and halves. With a half-angle identity, you can get the value of a sine for a 15-degree angle using a function of of 30 degree angle. You [more…]

### How to Find Half-Angle Identities for Tangent

The half-angle trig identity for tangent has two versions. Rather than this being a nuisance, having more than one option is really rather nice, because you can choose the version that works best for your [more…]

### Dealing with Half-Angle Identities Involving Radicals

By adding, subtracting, or doubling angle measures, you can find lots of exact values of trigonometry functions. For example, you can use the half-angle identity when the exact value of the trig function [more…]

### How to Find a Common Denominator of a Fraction to Solve a Trig Identity

Fractions are your friends. You may not believe this now, but the more you work with trigonometry functions, the more you’ll like fractions. Finding a common denominator to combine fractions often paves [more…]

### How to Multiply by a Conjugate to Find a Trigonometry Identity

Conjugates offer a great way to find trigonometry identities. In mathematics, a conjugate consists of the same two terms as the first expression, separated by the opposite sign. For instance, the conjugate [more…]

### How to Square Both Sides to Solve a Trigonometry Identity Problem

When you work on both sides of a trig identity at the same time, you may sometimes need to square both sides. You generally use this technique when one side or the other [more…]

### How to Work with Inverse Trigonometry Functions

The easiest way to work with inverse trig functions is to have a chart handy with the exact values of the functions. When angles other than the most common or popular are involved, you can either use a [more…]

### Toggle between Radians and Degrees on Your Scientific Calculator

Scientific calculators are very accommodating — they give you results in either degrees or radians, depending on which mode you set them in. This feature is great, but it trips up even the best mathematicians [more…]

### Use the Inverse Trigonometry Function or Inverse of a Reciprocal Function on Your Calculator

On scientific calculators, the –1 or *x*^{–}^{1} button means to find the reciprocal of a number. This reciprocal button allows you to find the value of a reciprocal function when you’re working with a number. [more…]

### How to Solve Inverse Trigonometry Functions with Uncommon Angles

When working with inverse trig functions, it’s always more convenient when the numbers you’re working with are the results of applying one of the trig functions to a common angle measure. When the angle [more…]

### Solve Trigonometry Equations by Factoring

The same type of factoring that algebra uses to solve equations is a great help in solving trigonometry equations. The only trick with the trig equations is to recognize that instead of just [more…]

### Solve a Trig Equation by Finding a Greatest Common Factor

The trigonometry equations that require finding a greatest common factor, factoring it out, and then solving the equation could look like one of the following two equations: [more…]

### How to Factor Trigonometry Expressions by Grouping

The process of factoring by grouping works in very special cases, when the original trigonometry expression is the result of multiplying two binomials together that have some unrelated terms in them. You [more…]

### How to Solve a Trigonometry Equation Using the Quadratic Formula

When trigonometry quadratic equations factor, life is good. When they don’t, you can still survive, thanks to that wonderful quadratic formula. In case you’ve forgotten the exact formula, here it is. [more…]

### How to Solve a Trig Equation That Has Multiple Trigonometry Functions

Some trigonometry equations contain more than one trig function. Others have mixtures of multiple angles and single angles with the same variable. Some examples of such equations include 3cos [more…]

### How to Find a Solution to a Multiple-Angle Trig Equation

Multiple-angle trigonometry expressions are those where the angle measure is some multiple of a variable — for example, 2*x* or 3*y*. You can take these expressions apart and solve for all the additional solutions [more…]

### How to Square Both Sides of a Trig Equation

When solving trigonometry equations, more than one method will usually work — although one method is often quicker or easier than another. With practice, you’ll get good at choosing the better of the ways [more…]

### How to Multiply through a Trig Equation with Another Function

The technique of multiplying through a trigonometry equation by a carefully selected function shouldn’t be your first choice — or your second, third, or fourth choice. This method is usually a last resort [more…]

### How to Solve a Trig Equation Using a Graphing Calculator

Some of the more-advanced graphing calculators make short work of solving trigonometry equations. A graphing calculator comes in very handy when the equation is complicated, has several different functions [more…]

### How to Use the Law of Sines with a Triangle

When you already know two angles in a triangle as well as one of the sides, such as in the case of ASA or AAS, you can use the *law of sines* to find the measures of the other two sides. This law uses the [more…]

### Use the Law of Cosines with a Triangle

The law of cosines comes in handy when you have two or more sides of a triangle — as in situations involving SSS and SAS — and need to use trigonometry to find the measures of the other three parts. When [more…]

### Use the Law of Cosines for SAS

When you have two sides of a triangle and the angle between them, otherwise known as SAS (side-angle-side), you can use the law of cosines to solve for the other three parts. Consider the triangle [more…]

### Use the Law of Cosines with SSS

When you know the values for two or more sides of a triangle, you can use the law of cosines. In the following case, you know all three sides (which is called SSS, or side-side-side, in trigonometry) but [more…]

### Use the Law of Cosines for SSA

The Law of Cosines works well for solving triangles when you have two sides and an angle, but the angle isn’t between the two sides. In this case, the Law of Sines isn’t an option. Also, to solve a triangle [more…]

### 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…]