About This Chapter
GACE Math: Trigonometric Identities - Chapter Summary
This chapter will help you review trigonometric identities and their applications before you take the GACE Mathematics assessment. Watch the short, engaging lesson videos so that you will be prepared for questions about:
- Basic and alternate forms of trigonometric identities
- Pythagorean identities and reciprocal identities
- Double-angle identities and half-angle identities
- Product-to-sum identities and sum-to-product identities
- Trigonometric equation identities
- Sum and difference identities
In addition to completing the lesson videos, take the lessons' practice quizzes to find any areas you don't fully grasp. Improve your understanding of these areas by reexamining the key spots in lesson videos that discussed them or reading over the lesson transcripts.
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 GACE Mathematics (522): Practice & Study Guide course
- GACE Math: Properties of Real Numbers
- GACE Math: Fractions
- GACE Math: Decimals & Percents
- GACE Math: Ratios & Proportions
- GACE Math: Measurements & Conversions
- GACE Math: Logic
- GACE Math: Mathematical Reasoning
- GACE Math: Vector Operations
- GACE Math: Matrices & Determinants
- GACE Math: Exponents & Exponential Expressions
- GACE Math: Algebraic Expressions
- GACE Math: Linear Equations
- GACE Math: Inequalities
- GACE Math: Absolute Value Problems
- GACE Math: Quadratic Equations
- GACE Math: Polynomials
- GACE Math: Rational Expressions
- GACE Math: Radical Expressions
- GACE Math: Systems of Equations
- GACE Math: Complex Numbers
- GACE Math: Functions
- GACE Math: Piecewise Functions
- GACE Math: Exponential & Logarithmic Functions
- GACE Math: Continuity of Functions
- GACE Math: Limits
- GACE Math: Rate of Change
- GACE Math: Calculating Derivatives & Derivative Rules
- GACE Math: Graphing Derivatives
- GACE Math: Applications of Derivatives
- GACE Math: Area Under the Curve & Integrals
- GACE Math: Integration Techniques
- GACE Math: Integration Applications
- GACE Math: Introduction to Geometric Figures
- GACE Math: Properties of Triangles
- GACE Math: Triangles, Theorems & Proofs
- GACE Math: Parallel Lines & Polygons
- GACE Math: Quadrilaterals
- GACE Math: Circular Arcs & Circles
- GACE Math: Conic Sections
- GACE Math: Geometric Solids
- GACE Math: Analytical Geometry
- GACE Math: Using Trigonometric Functions
- GACE Math: Trigonometric Graphs
- GACE Math: Solving Trigonometric Equations
- GACE Math: Sequences & Series
- GACE Math: Graph Theory
- GACE Math: Set Theory
- GACE Math: Overview of Statistics
- GACE Math: Summarizing Data
- GACE Math: Tables & Plots
- GACE Math: Probability
- GACE Math: Discrete Probability Distributions
- GACE Math: Continuous Probability Distributions
- GACE Math: Sampling
- GACE Math: Regression & Correlation
- GACE Mathematics Flashcards