# Ch 56: MTEL Math: Trigonometric Identities

### About This Chapter

## MTEL Math: Trigonometric Identities - Chapter Summary

The video lessons in this chapter will show how some identities can assist you in solving complex equations. These animated lessons can re-introduce you to the different types of trigonometric identities and remind you of their various uses. Discover how expressions and equations can be organized through the use of the Pythagorean identities, and recall the rules for writing half-angle identities or rewriting functions altogether. After viewing each of the lessons, you could:

- Understand the uses for trigonometric identities
- List trig identities that include sin and cos
- Identify alternate trig identities
- Describe the applications for Pythagorean identities
- Discuss the uses for sum-to-product, half-angle, product-to-sum, double-angle and reciprocal identities
- Prove a trigonometric equation identity
- Use sum and difference identities, and derive trig identities

Learn from accomplished instructors whose goal is to make it easy and fun to conquer these mathematical concepts. The chapter's video lessons are short and designed to fit into your schedule. They include graphics and narration along with several examples that you can go over multiple times as you strive to become an expert on trigonometric identities. Before taking on the MTEL Math examination's related questions, complete this chapter's short quizzes.

### MTEL Math: Trigonometric Identities Chapter Objectives

The five multiple-choice subareas on the MTEL Math examination include several sub-sections. Subarea V is titled Trigonometry, Calculus and Discrete Mathematics. It has 19 - 23 objectives, between 19 and 21 multiple-choice questions, and a 16% share of the test weighting. During its first sub-section, demonstrate your knowledge of the properties of trigonometric identities and the law of sine and cosine among other topics while going for a teaching license. Set aside four hours to answer the computerized certification examination's 100 multiple-choice questions and two open-response items.

### 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.

### 12. How to Prove & Derive Trigonometric Identities

After watching this video lesson, you will learn how some of our trigonometric identities are derived. You will also see how some identities naturally lead to the others.

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### Other Chapters

Other chapters within the MTEL Mathematics (09): Practice & Study Guide course

- MTEL Math: Basic Arithmetic Operations
- MTEL Math: Absolute Value & Integers
- MTEL Math: Fractions
- MTEL Math: Decimals
- MTEL Math: Percents
- MTEL Math: Rates & Ratios
- MTEL Math: Proportions
- MTEL Math: Estimation
- MTEL Math: Origins of Math
- MTEL Math: Rational & Irrational Numbers
- MTEL Math: Complex Numbers
- MTEL Math: Properties of Numbers
- MTEL Math: Exponents & Exponential Expressions
- MTEL Math: Roots & Radical Expressions
- MTEL Math: Scientific Notation
- MTEL Math: Number Theory
- MTEL Math: Number Patterns & Sequences
- MTEL Math: Number Patterns & Series
- MTEL Math: Properties of Functions
- MTEL Math: Graphing Functions
- MTEL Math: Factoring
- MTEL Math: The Coordinate Graph & Symmetry
- MTEL Math: Linear Equations
- MTEL Math: Systems of Linear Equations
- MTEL Math: Vectors, Matrices & Determinants
- MTEL Math: Introduction to Quadratics
- MTEL Math: Working with Quadratic Functions
- MTEL Math: Polynomial Functions Basics
- MTEL Math: Higher-Degree Polynomial Functions
- MTEL Math: Piecewise, Absolute Value & Step Functions
- MTEL Math: Rational Expressions, Functions & Graphs
- MTEL Math: Exponential & Logarithmic Functions
- MTEL Math: Measurement
- MTEL Math: Perimeter & Area
- MTEL Math: Polyhedrons & Geometric Solids
- MTEL Math: Symmetry, Similarity & Congruence
- MTEL Math: Properties of Lines
- MTEL Math: Angles
- MTEL Math: Triangles
- MTEL Math: Triangle Theorems & Proofs
- MTEL Math: Similar Polygons
- MTEL Math: The Pythagorean Theorem
- MTEL Math: Quadrilaterals
- MTEL Math: Circles
- MTEL Math: Circular Arcs & Measurement
- MTEL Math: Analytic Geometry & Conic Sections
- MTEL Math: Polar Coordinates & Parameterization
- MTEL Math: Transformations
- MTEL Math: Data & Graphs
- MTEL Math: Statistics
- MTEL Math: Data Collection
- MTEL Math: Samples & Populations
- MTEL Math: Probability
- MTEL Math: Trigonometric Functions
- MTEL Math: Graphs of Trigonometric Functions
- MTEL Math: Applications of Trigonometry
- MTEL Math: Limits
- MTEL Math: Continuity
- MTEL Math: Rate of Change
- MTEL Math: Derivative Calculations & Rules
- MTEL Math: Graphing Derivatives & L'Hopital's Rule
- MTEL Math: Area Under the Curve & Integrals
- MTEL Math: Integration Techniques
- MTEL Math: Integration Applications
- MTEL Math: Differential Equations
- MTEL Math: Discrete & Finite Math
- MTEL Mathematics Flashcards