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# Trigonometry

## Explore trigonometry through identities, polar graphing, and solving triangles.

This course will teach you the all of the fundamentals of trigonometry, starting from square one: the basic idea of similar right triangles. In the first sequences in this course, you'll learn the definitions of the most common trigonometric functions from both a geometric and algebraic perspective.

In this course, you'll master trigonometry by solving challenging problems and interacting with animated graphs, not by relying on rote memorization. Additionally, you'll learn how to apply trigonometry in the contexts of measuring and manipulating sound waves and creating complex, artistic designs using polar graphing.

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1. 1

### Introduction to Trigonometry

1. #### Exploring the Sine

Understand the sine function and how it gets used.

2. #### Graphing the Sine

What does the graph of the sine function look like?

3. #### Thinking in Polar

Use distance and angles to graph with circles and reveal new patterns.

2. 2

### The Functions of Trigonometry

Learn the six basic trig functions in an intuitive way.

1. Included with

Get acquainted with two ways to measure an angle.

2. Included with

#### Optional: Greek Letter Primer

Use this tutorial to get comfortable with Greek letters, which are common in trigonometry.

3. Included with

#### Sine and Cosine

Explore the fundamental properties of the two fundamental trigonometry functions.

4. Included with

#### The Unit Circle

Create a reference tool to help find the exact value of trig functions.

3. 3

### Measuring

Use trigonometry functions to solve for sides and angles.

1. Included with

#### Solving Right Triangles

Apply what you've learned about sine, cosine, and tangent to find missing sides of triangles.

2. Included with

#### Solving for Angles

Invert trigonometry functions to solve for angles instead of sides.

3. Included with

#### Law of Sines

Calculate side lengths and angle measures on any triangle, not just right triangles.

4. Included with

#### Law of Cosines

Learn a Law that works when Law of Sines doesn't

4. 4

### Cartesian Graphing

Explore how trig graphs work on the traditional x-y plane.

1. Included with

#### Trigonometry Graphs

What do the graphs of sine and cosine look like?

2. Included with

#### Frequency and Phase Shift

Explore the basic attributes of waves.

3. Included with

When you add two sine functions, sometimes it makes a mess and other times it just makes another sine.

4. Included with

#### Other Trigonometry Function Graphs

Explore some unusual trigonometry graphs, including secant and cosecant.

5. 5

### Polar Graphing

Plot on a circle rather than a grid for some spectacular graphs.

1. Included with

#### Polar Intro

Explore a new method of graphing that uses angle and distance as the two independent variables.

2. Included with

#### Basic Polar Flowers

Make flowers using sine and cosine.

3. Included with

#### More Flowers

Build up your skills with polar graphing by creating and understanding more complex flowers.

4. Included with

#### Cardioids and Limacons

Investigate two special classes of polar graphs that look like hearts and beans.

6. 6

### Identities

Use substitutions to transform and simplify trig expressions.

1. Included with

#### Reciprocal Identities

Launch into identities based on this set derived directly from the definitions of the six trig functions.

2. Included with

#### Quotient Identities

Relate sine and cosine with tangent to enable changing between different trig functions.

3. Included with