# Ch 9: Big Ideas Math Algebra 2 - Chapter 9: Trigonometric Ratios and Functions

### About This Chapter

## How It Works:

- Find the lesson within this chapter that corresponds to what you're studying in the Trigonometric Ratios and Functions chapter of your textbook.
- Watch fun videos that cover the trigonometric ratio and function concepts you need to learn or review.
- Complete the quiz after watching each video lesson to test your understanding.
- If you need additional help, rewatch the videos until you've mastered the material, or submit a question for one of our instructors.

## Chapter Topics

You'll learn all of the algebra topics covered in the textbook chapter, including:

- Identifying the six main trigonometric functions
- Using the Pythagorean Theorem for functions
- What special angles are and their trigonometric value
- Using sine, cosine and tangent
- Defining terminal side and initial side
- What the parts of a circle are and how to use them
- Graphing sine, cosine and tangent functions
- How to find the sinusoidal function
- What trigonometric identities are and their uses
- How to apply the sum and difference identities

*Big Ideas Math is a registered trademark of Larson Texts, Inc., which is not affiliated with Study.com.*

### 1. Trigonometric Functions: Definition & Examples

In mathematics, trigonometric functions are functions of angles. This lesson will describe the 6 main trigonometric functions, use them to solve problems, and give some examples. The quiz at the end of the lesson will allow you to practice what you've learned.

### 2. Trigonometry and the Pythagorean Theorem

Explore how the Pythagorean Theorem can be used in conjunction with trigonometric functions. In this lesson, take an inverse trigonometric function, and define all three sides of a right triangle.

### 3. Trigonometric Function Values of Special Angles

After watching this video lesson, you will better understand the six trigonometric functions. You will also know what special angles there are and what the trigonometric values for these special angles are.

### 4. Practice Finding the Trigonometric Ratios

So you know what sine, cosine and tangent are. Great! But how do you use them? Find out how in this lesson as we find missing sides and angles using trigonometric ratios.

### 5. Drawing Angles in Standard Position

Angles can be drawn facing any direction you want, but when you put them in standard position, it's easier to estimate the angle measure and work with them using graphs and coordinates. In this lesson, we'll explore drawing angles in standard position.

### 6. Coterminal Angles: Definition & Examples

This lesson defines coterminal angles measured in degrees. You will learn how to calculate positive and negative coterminal angles with a few examples.

### 7. Radian Measure: Definition & Formula

In mathematics, the radian is the standard unit of angular measure. This lesson will define radian and work through some problems involving radians. The lesson will end with a quiz.

### 8. Arc Length of a Sector: Definition and Area

In this lesson, we'll slice up a circle like it's a pizza and learn how to find out useful information about our slices. We'll find out the area of these sectors, or pie slices. We'll also learn about arc lengths.

### 9. Using Unit Circles to Relate Right Triangles to Sine & Cosine

The unit circle is a helpful tool for understanding trigonometric concepts. In this lesson, we'll look at right triangles on the unit circle to better grasp sine and cosine.

### 10. Unit Circle: Memorizing the First Quadrant

Memorizing the unit circle can be a daunting task, but this lesson will show you a pattern to help you memorize the points, degree measures, and radian measures for the entire first quadrant.

### 11. Reference Angles & the Unit Circle

Watch this video lesson to learn how you can use the unit circle and its reference angles to help you solve trigonometry problems. Learn how to find your answers from the unit circle.

### 12. Graphing Sine and Cosine

Sine and cosine aren't just for triangles; they can also be waves. See them graphed on the unit circle and then learn how that translates into the sine and cosine waves.

### 13. Graphing Sine and Cosine Transformations

What happens when we take the sine and cosine wave and transform them? They get bigger, smaller, faster and slower. Find out how in this lesson on sine and cosine wave transformations.

### 14. Graphing the Tangent Function: Amplitude, Period, Phase Shift & Vertical Shift

Take a look at how the graph of a tangent function and how we can transform it by making a few small changes to its equation. This video shows how to graph the original function and explains its transformations.

### 15. Graphing the Cosecant, Secant & Cotangent Functions

After watching this video lesson, you will learn what the graphs of the cosecant, secant, and cotangent trigonometric functions look like. You will also learn how to see if these graphs are shifted or transformed.

### 16. Finding the Sinusoidal Function

After watching this video lesson, you will be able to write a sinusoidal function to represent any wave that you see. Learn what parts of the function make the wave shift up, down, to the left, and to the right.

### 17. 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.

### 18. 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.

### 19. 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 Big Ideas Math Algebra 2: Online Textbook Help course

- Big Ideas Math Algebra 2 - Chapter 1: Linear Functions
- Big Ideas Math Algebra 2 - Chapter 2: Quadratic Functions
- Big Ideas Math Algebra 2 - Chapter 3: Quadratic Equations and Complex Numbers
- Big Ideas Math Algebra 2 - Chapter 4: Polynomial Functions
- Big Ideas Math Algebra 2 - Chapter 5: Rational Exponents and Radical Functions
- Big Ideas Math Algebra 2 - Chapter 6: Exponential and Logarithmic Functions
- Big Ideas Math Algebra 2 - Chapter 7: Rational Functions
- Big Ideas Math Algebra 2 - Chapter 8: Sequences and Series
- Big Ideas Math Algebra 2 - Chapter 10: Probability
- Big Ideas Math Algebra 2 - Chapter 11: Data Analysis and Statistics