# Ch 46: NES Math: Trigonometric Identities

### About This Chapter

## NES Math: Trigonometric Identities - Chapter Summary

Let us support your review of trigonometric identities and their uses while you get ready for the related part of the NES Math test. Our snappy lessons cover topics such as:

- Definition of trigonometric identities and their purpose
- Basic trigonometric identities and alternate forms
- Applications and uses of various types of identities, including Pythagorean, reciprocal, double- and half-angle
- How to verify a trigonometric equations identity
- How to apply the sum and difference identities

Available 24/7 via computer, tablet or smartphone, these video lessons average about five minutes in length. After you watch them, you can test your understanding with short lesson quizzes and a more comprehensive chapter exam. Clickable links back to specific parts of the lesson make it easy to review and discover where you need more study. Our expert instructors use plenty of examples, practice problems and humor to make the lessons entertaining, and you can contact them through our message board if you have questions.

### NES Math: Trigonometric Identities Chapter Objectives

The NES Math test, used in five states as a requirement for teacher certification in mathematics, is a computer-delivered exam consisting entirely of multiple-choice questions. The quizzes that accompany each of our lessons are in the same format and will provide good practice for what you'll face on test day.

Questions on the NES test are divided into five content domains. Trigonometric identities are covered in the content domain on trigonometry and calculus, which makes up 19% of the test's total score.

### 1. Trigonometric Identities: Definition & Uses

After watching this video lesson, you will understand what a trigonometric identity is. You will also know the different kinds of identities you will come across.

### 2. List of the Basic Trig Identities

There are specific trig functions that have very special and very simple relationships with each other. Learn the main one and how you can use it to understand the others.

### 3. Alternate Forms of Trigonometric Identities

After watching this video lesson, you will know some of the alternate forms of the basic trigonometric identities. You will also learn how to use these alternate forms.

### 4. Pythagorean Identities: Uses & Applications

After watching this video lesson, you will be able to spot the Pythagorean identities when you see them. You will also learn how these identities can help you solve more complicated trig problems.

### 5. Reciprocal Identities: Uses & Applications

Trigonometry is full of identities, a set of which are called the reciprocal identities. Watch this video lesson to learn what they are and how you can use them to help you solve problems.

### 6. Double-Angle Identities: Uses & Applications

Watch this video lesson to learn how you can use the double-angle identities in trigonometry to help you prove and solve more complicated trigonometry problems.

### 7. Half-Angle Identities: Uses & Applications

After watching this video lesson, you will be able to use half-angle identities to help you simplify your trig problems and also to help you prove other trig statements.

### 8. Product-to-Sum Identities: Uses & Applications

After watching this video lesson, you will know what the four product-to-sum identities are. You will also know how they are used. You will also see two examples of problems.

### 9. Sum-to-Product Identities: Uses & Applications

In this video lesson, you will learn about the four sum-to-product identities for the sine and cosine functions. Learn how to go from the sum or subtraction of two functions to the product of two functions along with the two angles.

### 10. Verifying a Trigonometric Equation Identity

Watch this video lesson to learn how you can use your basic definitions and identities to help you prove a trigonometric equation identity. Learn what is involved and what to do for a successful answer.

### 11. Applying the Sum & Difference Identities

Watch this video lesson to learn the six sum and difference identities for the trig functions of sine, cosine, and tangent. Also, learn how you can use them to your advantage when solving tough trig problems.

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### Other Chapters

Other chapters within the NES Mathematics (304): Practice & Study Guide course

- NES Math: Properties of Real Numbers
- NES Math: Fractions
- NES Math: Decimals & Percents
- NES Math: Ratios & Proportions
- NES Math: Units of Measure & Conversions
- NES Math: Logic
- NES Math: Reasoning
- NES Math: Vector Operations
- NES Math: Matrix Operations & Determinants
- NES Math: Exponents & Exponential Expressions
- NES Math: Algebraic Expressions
- NES Math: Linear Equations
- NES Math: Inequalities
- NES Math: Absolute Value
- NES Math: Quadratic Equations
- NES Math: Polynomials
- NES Math: Rational Expressions
- NES Math: Radical Expressions
- NES Math: Systems of Equations
- NES Math: Complex Numbers
- NES Math: Functions
- NES Math: Piecewise Functions
- NES Math: Exponential & Logarithmic Functions
- NES Math: Continuity of Functions
- NES Math: Limits
- NES Math: Rate of Change
- NES Math: Derivative Rules
- NES Math: Graphing Derivatives
- NES Math: Applications of Derivatives
- NES Math: Area Under the Curve & Integrals
- NES Math: Integration Techniques
- NES Math: Applications of Integration
- NES Math: Foundations of Geometry
- NES Math: Geometric Figures
- NES Math: Properties of Triangles
- NES Math: Triangle Theorems & Proofs
- NES Math: Parallel Lines & Polygons
- NES Math: Quadrilaterals
- NES Math: Circles & Arc of a Circle
- NES Math: Conic Sections
- NES Math: Geometric Solids
- NES Math: Analytical Geometry
- NES Math: Trigonometric Functions
- NES Math: Trigonometric Graphs
- NES Math: Solving Trigonometric Equations
- NES Math: Sequences & Series
- NES Math: Graph Theory
- NES Math: Set Theory
- NES Math: Statistics Overview
- NES Math: Summarizing Data
- NES Math: Tables, Plots & Graphs
- NES Math: Probability
- NES Math: Discrete Probability Distributions
- NES Math: Continuous Probability Distributions
- NES Math: Sampling
- NES Math: Regression & Correlation
- NES Mathematics Flashcards