# Ch 46: PLACE Mathematics: Trigonometric Identities

### About This Chapter

## PLACE Mathematics: Trigonometric Identities - Chapter Summary

You can use the lessons in this chapter to review trigonometric identities so that you are prepared for questions on the PLACE Mathematics exam. Our videos review all the important concepts, highlighting the most important points, to refresh your memory. The videos cover these topics:

- Uses of trigonometric identities
- Basic and alternate trigonometric identities
- Pythagorean and reciprocal identities
- Double and half-angle identities
- Product-to-sum and sum-to-product identities
- Verifying a trigonometric equation identity
- Applying sum and difference identities

Our knowledgeable instructors review each of the concepts and highlight the most important points that you need to know for the test. By using multiple approaches, the process of familiarizing yourself with the material becomes easier and more enjoyable.

### Objectives of the PLACE Mathematics: Trigonometric Identities Chapter

The PLACE Mathematics Exam is a test that evaluates your knowledge and understanding of all aspects of mathematics, including foundations of mathematics, functions and relations, measurement and geometry, probability and statistics, and calculus and discrete mathematics. The topics covered in this Trigonometric Identities chapter fall within the Functions and Relations section which includes 24% of the test questions. The self-assessment quizzes that accompany each lesson allow you to test your knowledge and give you a feel for the types of questions that appear on the actual exam.

All of the questions on the exam are multiple choice. You will read a problem or question and then review several possible response options from which you need to select the single correct answer.

### 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 PLACE Mathematics: Practice & Study Guide course

- PLACE Mathematics: Properties of Real Numbers
- PLACE Mathematics: Fractions
- PLACE Mathematics: Decimals & Percents
- PLACE Mathematics: Ratios & Proportions
- PLACE Mathematics: Measurements & Conversions
- PLACE Mathematics: Logic
- PLACE Mathematics: Mathematical Reasoning
- PLACE Mathematics: Vector Operations
- PLACE Mathematics: Matrices & Determinants
- PLACE Mathematics: Exponents & Exponential Expressions
- PLACE Mathematics: Algebraic Expressions
- PLACE Mathematics: Linear Equations
- PLACE Mathematics: Inequalities
- PLACE Mathematics: Absolute Value Problems
- PLACE Mathematics: Quadratic Equations
- PLACE Mathematics: Polynomials
- PLACE Mathematics: Rational Expressions
- PLACE Mathematics: Radical Expressions
- PLACE Mathematics: Systems of Equations
- PLACE Mathematics: Complex Numbers
- PLACE Mathematics: Functions
- PLACE Mathematics: Graphing Piecewise Functions
- PLACE Mathematics: Exponential and Logarithmic Functions
- PLACE Mathematics: Continuity of Functions
- PLACE Mathematics: Limits
- PLACE Mathematics: Rate of Change
- PLACE Mathematics: Calculating Derivatives & Derivative Rules
- PLACE Mathematics: Graphing Derivatives & L'Hopital's Rule
- PLACE Mathematics: Applications of Derivatives
- PLACE Mathematics: Area Under the Curve & Integrals
- PLACE Mathematics: Integration & Integration Techniques
- PLACE Mathematics: Integration Applications
- PLACE Mathematics: Foundations of Geometry
- PLACE Mathematics: Introduction to Geometric Figures
- PLACE Mathematics: Properties of Triangles
- PLACE Mathematics: Triangles, Theorems & Proofs
- PLACE Mathematics: Parallel Lines & Polygons
- PLACE Mathematics: Quadrilaterals
- PLACE Mathematics: Circular Arcs & Circles
- PLACE Mathematics: Conic Sections
- PLACE Mathematics: Geometric Solids
- PLACE Mathematics: Analytical Geometry
- PLACE Mathematics: Using Trigonometric Functions
- PLACE Mathematics: Trigonometric Graphs
- PLACE Mathematics: Solving Trigonometric Equations
- PLACE Mathematics: Sequences & Series
- PLACE Mathematics: Graph Theory
- PLACE Mathematics: Set Theory
- PLACE Mathematics: Overview of Statistics
- PLACE Mathematics: Summarizing Data
- PLACE Mathematics: Tables & Plots
- PLACE Mathematics: Probability
- PLACE Mathematics: Discrete Probability Distributions
- PLACE Mathematics: Continuous Probability Distributions
- PLACE Mathematics: Sampling
- PLACE Mathematics: Hypothesis Testing
- PLACE Mathematics: Regression & Correlation
- PLACE Mathematics Flashcards