# Overview of Trigonometry

Okay, we are a bit biased, but we think Trig is super cool. Hear us out. We used to dislike math and trig, too! But after realizing some secrets and the shortcuts to mastering math we developed a deep love for Trig. Really we think the most important thing is understanding and knowing your Unit Circle. This is going to be your guide and best friend.

#### History of Trig

Trigonometry stems from the study of triangles. Triangles have been used and understood since roughly 2000 years Before Christ. Triangles were used both in Egyptian and Babylonian mathematics. Imagine that! And we still use triangles to this day in Austin Texas! During the Middle Ages Islamic mathematicians knew the six trigonometric functions! This is really impressive. Another reason that we are fascinated by trigonometry is because so many different cultures have had an impact on shaping and practicing it. Chinese and Indian mathematicians also used trigonometry and added to today’s notion of modern trig.

What’s Tough about Trig

Understanding and learning the trig functions is super important for trig. Knowing the Unit Circle by heart—and understanding the sin/cos ratios. We think that many students miss out on these core ideas. They don’t fully appreciate how important it is to know them and be able to use them quickly. But eventually many students end up finding trigonometry more enjoyable than Algebra. We agree! We like Trig a lot. We think that our approach to trig makes it easier to understand. We don’t encourage rote memorization of the material, as some other professors do. We encourage students to think about the big ideas in trig. We want them to *understand* and know why they are doing the math they’re doing.

#### Expectations for Your Trig Course

In your trig course you can expect to study a few things. We have listed them out for you here. Don’t get worried. Just plug away and start trying to practice and learn a few of these concepts. At its foundation, Trigonometry is a study of the unit circle and trigonometric functions. Therefore, you should devote extra time to studying and understanding those areas. Whether you’re reading from Austin Texas or anywhere else in the United States, your trigonometry class will also most certainly include the common trigonometric equations and identities. These are topics which we urge you not to memorize. Granted, you should learn some of the key common trig identities and the relationships between them, but don’t go around memorizing lists and lists of identities. Many students get tripped up with this.

Unit Circle

The Trigonometric Functions

Trig Equations & Identities

Triangles & Trig