**Algebra & Trigonometry**

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### Algebra and Trigonometry Course Outline

### What are the prerequisite to algebra and trigonometry?

Concepts Covered:

- Why are real numbers an algebra essentials?
- What is the difference between exponents and scientific notation?
- What is the difference between radicals and rational expressions?
- What are polynomials?
- How are polynomials factored?
- What are rational expressions?

### How do equations relate to inequalities?

Concepts Covered:

- How are rectangular coordinate systems applied to graphs?
- How to use linear equations with one variable?
- How are models and applications in algebra and trigonometry apply to real-world situations?
- What are different ways to solve complex numbers?
- What are different ways to solve quadratic equations?
- What are other types of equations used in algebra and trigonometry?
- What is the difference between linear inequalities and absolute value inequalities?

### What are functions?

Concepts Covered:

- How are function notation applied in functions?
- What is the difference between domain and range?
- How does the rate of change affect the behavior of graphs?
- How do you find the composition of functions?
- How can functions be transformed?
- How do you find absolute value functions?
- What are inverse functions?

### What are linear functions?

Concepts Covered:

- How do we use linear functions?
- How do we model linear functions?
- How do we fit linear models to data?

### How are polynomials related to rational functions?

Concepts Covered:

- How are quadratic functions applied in parabolas?
- What is the difference between power functions and polynomial functions?
- Why do we graph polynomial functions?
- How do we divide polynomials?
- How do we find zeros in polynomial functions?
- Why are rational functions important?
- What is the difference between inverses and radical functions?
- How do we model using variations?

### What are exponential and logarithmic functions?

Concepts Covered:

- How are exponential functions used?
- How do we graph exponential functions?
- How do we find logarithmic functions?
- How do we graph logarithmic functions?
- What are logarithmic properties?
- What is the difference between exponential and logarithmic equations?
- How do we use exponential and logarithmic models?
- How do we use data to fit exponential models?

### What is the difference between sine and cosine functions?

Concepts Covered:

- How are angles used in algebra and trigonometry?
- How do we use right triangles in algebra and trigonometry?
- What is a unit circle?
- What are some other trigonometric functions?

### What are periodic functions?

Concepts Covered:

- How do you make graphs with sine and cosine functions?
- How do you make graphs with other trigonometric functions?
- What are inverse trigonometric functions?

### How do trigonometric identities affect equations?

Concepts Covered:

- How do we solve trigonometric equations with identities?
- How do we compare sum and difference identities?
- How do we differentiate double-angle, half-angle, and reduction formula identities?
- What is the difference between sum-to-product and product-to-sum formulas?
- How do we solve trigonometric equations?

### What else is there in trigonometry?

Concepts Covered:

- How do non-right triangles relate to the law of sines?
- How do non-right triangles relate to the law of cosines?
- How are polar coordinates used?
- How are polar coordinates graphed?
- What is the polar form of complex numbers?
- How are parametric equations formed?
- How are parametric equations graphed?
- What are vectors?

### How do the systems of equations and inequalities operate?

Concepts Covered:

- How do you use the systems of linear equations using two variables?
- How do you use the systems of linear equations using three variables?
- What are the two variables in the systems of nonlinear equations and inequalities?
- Why do we get partial fractions?
- What is the difference between the matrices and matrix operations?
- How do we solve different systems with the Gaussian elimination?
- How do we solve different systems with inverses?
- How do we solve different systems using Cramer’s rule?

### What is analytic geometry?

Concepts Covered:

- How is an ellipse formed?
- What is a hyperbola?
- How do we form parabolas?
- What are the rotation of axes?
- Where are the conic sections in the polar coordinates?

### How do sequences, probability, and counting theory relate to each other?

Concepts Covered:

- How do we find sequences and their notations?
- How do we find arithmetic sequences?
- How do we find geometric sequences?
- How do we find series and their notations?
- How do we count problems with principles?
- What is binomial theorem?
- What is probability?

Algebra and Trigonometry provides a comprehensive exploration of algebraic principles and meets scope and sequence requirements for a typical introductory algebra and trigonometry course. The modular approach and the richness of content ensure that the book meets the needs of a variety of courses. Algebra and Trigonometry offers a wealth of examples with detailed, conceptual explanations, building a strong foundation in the material before asking students to apply what they’ve learned.

**About the authors:**

## Senior Contributing Authors

**Jay Abramson,** Arizona State University

## Contributing Authors

Valeree Falduto, Palm Beach State College

Rachael Gross, Towson University

David Lippman, Pierce College

Melonie Rasmussen, Pierce College

Christina Fernandez

Harold Whipple, Formerly of Columbia College

Jean-Marie Magnier, Springfield Technical Community College

Rick Norwood, East Tennessee State University

Nicholas Belloit, Florida State College at Jacksonville

## Assessment Question Author

**Dr. Angela Everett**Professor of Mathematics

**Chattanooga State Community College**