About This Chapter
ORELA Math: Trigonometric Identities - Chapter Summary
As you work your way through these quick, fun video lessons in preparation for the exam, you'll cover the trigonometric identities concepts ORELA-certified math educators are expected to have mastered. Lesson topics include:
- Basic and alternate forms of trig identities
- Pythagorean and reciprocal identities
- Double-angle and half-angle identities
- Product-to-sum and sum-to-product identities
- How to verify a trig equation identity
- Applications of sum and difference identities
The video transcripts present the most important terms and ideas in bold, making it easy to find the topics you'd like to review a second or third time. Use the lesson quizzes to see how well you've retained the information. If you have any questions about trigonometric identities, don't hesitate to ask our instructors for help.
ORELA Math: Trigonometric Identities Chapter Objectives
If you need help reviewing trigonometric identities for the ORELA Math exam, you've come to the right place. This chapter offers a bevy of useful resources to help you master the concepts you'll likely be tested on during the assessment. Lesson quizzes evaluate your exam-readiness and also introduce you to the ORELA format.
Trigonometry and calculus topics, like those highlighted here, cover 19% of the questions on the exam. You'll also be tested on four other areas: statistics, probability and discrete mathematics (19%); measurement and geometry (19%); mathematical processes and number sense (19%); trigonometry and calculus (19%); and patterns, algebra and functions (24%). There are approximately 150 tasks on the assessment. You'll have four and a quarter hours to complete all of them.
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 within the ORELA Mathematics: Practice & Study Guide course
- ORELA Math: Properties of Real Numbers
- ORELA Math: Fractions
- ORELA Math: Decimals & Percents
- ORELA Math: Ratios & Proportions
- ORELA Math: Units of Measure & Conversions
- ORELA Math: Logic
- ORELA Math: Reasoning
- ORELA Math: Vector Operations
- ORELA Math: Matrix Operations & Determinants
- ORELA Math: Exponents & Exponential Expressions
- ORELA Math: Algebraic Expressions
- ORELA Math: Linear Equations
- ORELA Math: Inequalities
- ORELA Math: Absolute Value
- ORELA Math: Quadratic Equations
- ORELA Math: Polynomials
- ORELA Math: Rational Expressions
- ORELA Math: Radical Expressions
- ORELA Math: Systems of Equations
- ORELA Math: Complex Numbers
- ORELA Math: Functions
- ORELA Math: Piecewise Functions
- ORELA Math: Exponential & Logarithmic Functions
- ORELA Math: Continuity of a Function
- ORELA Math: Limits
- ORELA Math: Rate of Change
- ORELA Math: Calculating Derivatives & Derivative Rules
- ORELA Math: Graphing Derivatives
- ORELA Math: Applications of Derivatives
- ORELA Math: Area Under the Curve & Integrals
- ORELA Math: Integration Techniques
- ORELA Math: Applications of Integration
- ORELA Math: Foundations of Geometry
- ORELA Math: Geometric Figures
- ORELA Math: Properties of Triangles
- ORELA Math: Triangle Theorems & Proofs
- ORELA Math: Parallel Lines & Polygons
- ORELA Math: Quadrilaterals
- ORELA Math: Circles & Arc of a Circle
- ORELA Math: Conic Sections
- ORELA Math: Geometric Solids
- ORELA Math: Analytical Geometry
- ORELA Math: Trigonometric Functions
- ORELA Math: Trigonometric Graphs
- ORELA Math: Solving Trigonometric Equations
- ORELA Math: Sequences & Series
- ORELA Math: Graph Theory
- ORELA Math: Set Theory
- ORELA Math: Statistics Overview
- ORELA Math: Summarizing Data
- ORELA Math: Tables, Plots & Graphs
- ORELA Math: Probability
- ORELA Math: Discrete Probability Distributions
- ORELA Math: Continuous Probability Distributions
- ORELA Math: Sampling
- ORELA Math: Regression & Correlation
- ORELA Mathematics Flashcards