Unit 2 Unit Circle Trigonometry

A guide for those starting the Pre-Calculus curriculum

By Damian Ferraro and Drew Davenport

Introduction to Unit Circle Trigonometry

Concepts of the Unit:

- Unit Circle

- Sinusoids

- Rotary Motion

Real Life Applications

Sample Problems

Introduction

For all of you, this unit is rich with familiar terms that you have heard of before. Remember 30 - 60 - 90 triangles and sine and cosine? Those will all be in this unit. What the bulk of this area of Pre-Calc talks about is the unit circle itself, and how it reflects a true diagram of sin, cos, tan, and the inverse functions of csc, sec, and cot. In this unit, you will discover news ways to incorporate sin and cos into your wide range of knowledge in mathematics.

Some unfamiliar terms that you will learn are sinusoidal graphs, rotary motion, and the double and half angle formulas. All of these incorporate the six trig functions, and especially sin and cos. You will learn how the graphs of sine and cosine play a role in the way that they work, and learn ways to use these equations to solve for variables.

Now, we know that was a lot of different topics and aspects of Pre-Calc that you guys do not understand yet, but we hope that through this website, we can give you an overview on Unit Circle Trigometry, and how it plays a major role in understand trig functions and problems that come along with them.

Concepts of the Unit

Let's start with the Unit Circle!

As you can see, there are a lot of numbers, but its a lot less complicated when you think about how we got these numbers:

Sine and cosine act as x and y, almost as if they are creating axises for themselves.
Radians (or the values inside the circle) are an alternate way of thinking about degrees.
Imagine that this unit circle has a radius of one, and then there are so many other values that can be calculated, just knowing the knowledge of 45-45-90 triangles and 30-60-90 triangles.
The values on the outside of the circle are an ordered pair (x, y), but in unit circle trigonometry, the ordering pair is (cos, sin)

This unit circle lays out a completely new structure to understanding how concepts that you learned in Geometry and Algebra II have a significance in your Pre-Calc class.

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