# Ch 22: Trigonometric Functions & Equations

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### About This Chapter

## Trigonometric Functions & Equations - Chapter Summary

The lessons in this chapter examine the basic functions and equations used in trigonometry, with examples and quizzes to help you grasp these concepts. Our instructors explain the laws of sine and cosine and how to use them and describe other trigonometric functions.

You'll see how to relate right triangles to sine and cosine, and look at the properties of special right triangles. Other lessons include practice problems with circular trigonometric functions, and there's also a list of the basic trig identities. Once you've completed these lessons, you should be ready to:

- Graph sine and cosine functions
- Identify cotangent, secant and cosecant
- Consider amplitude, period, phase shift and vertical shift when graphing the tangent function
- Relate right triangles to sine and cosine through the use of unit circles
- Utilize the double angle formula
- Convert between radians and degrees
- Solve trigonometric equations for
*x* - Use a calculator for trigonometric functions and exponentials

You'll enjoy learning about these topics through fun videos led by our expert instructors. The quizzes at the end of each lesson will aid in your understanding of what you've studied, and a jump feature in the timeline makes it easy to return to topics that require a little more attention. If you have questions, you can contact the instructor. Each lesson also includes a written transcript, so you can read along if that's how you learn best.

### 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. Law of Sines: Definition and Application

Don't get stuck trying to find missing sides or angles in a triangle. Use the Law of Sines to rescue you from any perilous triangle in which you have just a few pieces of information.

### 3. Law of Cosines: Definition and Application

In this lesson, we'll learn how to solve problems involving three sides and one angle in a triangle. The Law of Cosines, a modification of the Pythagorean Theorem, will save the day.

### 4. 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.

### 5. Other Trigonometric Functions: Cotangent, Secant & Cosecant

After watching this video lesson, you will understand how the trigonometric functions cotangent, secant, and cosecant are related to the sine, cosine, and tangent functions.

### 6. 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.

### 7. 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.

### 8. 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.

### 9. Practice Problems with Circular Trigonometric Functions

After watching this video lesson, you will be able to use the unit circle to help you find your answer to trig problems without making too many calculations. Watch and learn how you can find your angle in radians on the unit circle.

### 10. Special Right Triangles: Types and Properties

Not all right triangles are the same. In this lesson, we'll look at two special right triangles (30-60-90 and 45-45-90) that have unique properties to help you quickly and easily solve certain triangle problems.

### 11. The Double Angle Formula

When you encounter a doubled angle, there are special formulas that can help you handle trigonometric value. In this lesson, we'll define and practice using the double angle formulas for sine, cosine and tangent.

### 12. Converting Between Radians and Degrees

Angles can be measured in degrees or radians. This lesson will explore the difference and provide you with a simple calculation that can be used to convert degrees into radians and radians into degrees.

### 13. How to Solve Trigonometric Equations for X

Adding trigonometric functions into standard algebra equations adds complexity. Learn how to solve trigonometric equations for x and how to use inverse operations to simplify equations.

### 14. 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.

### 15. Trigonometry Functions & Exponentials on the CLEP Calculator

In this lesson, review how to use the history on the CLEP calculator as we calculate sines, cosines and the inverse trigonometric functions. Finish by exploring exponentials and logarithms.

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### Other Chapters

Other chapters within the Accuplacer College Level Math Test: Practice & Study Guide course

- Operations with Basic Algebraic Expressions
- Arithmetic with Rational Expressions
- Factoring in Algebra
- Expanding Polynomials
- Manipulating Roots
- Working with Exponents & Exponential Expressions
- Solving & Graphing Linear Equations
- Quadratic Equations
- Calculating & Graphing Inequalities
- Solving Systems of Linear Equations
- Geometric Angles & Shapes
- Conics in Algebra
- Algebraic Concepts of Groups & Sets
- Graphs of Algebraic Functions
- Complex and Imaginary Numbers
- Notation, Sequences & Series
- Matrices and Determinants in Algebra
- Combinatorics
- Fractions, Decimals & Mixed Numbers
- Approaches to Math Word Problems
- Understanding Exponential & Logarithmic Functions