- Subject:
- Mathematics
- Material Type:
- Module
- Provider:
- Ohio Open Ed Collaborative
- Tags:

- License:
- Creative Commons Attribution-NonCommercial 4.0
- Language:
- English
- Media Formats:
- Text/HTML

# Chapter 10.2 - Exercises

# Khan Academy - The Unit Circle

# Khan Academy - Cosine and Sine Functions

# The Unit Circle and Cosine and Sine Functions

## Module Overview

**TMM 002 PRECALCULUS** (Revised March 21, 2017)

**2. Geometry**

** 2b**. Analyze right triangles. Routine analysis of side lengths and angle measurements using trigonometric ratios/functions as well as the Pythagorean Theorem.*

Sample Tasks:

- The student can solve right triangles numerically using trigonometric ratios and relationships.
- The student can compare similar triangles numerically.
- The student can describe relationships within or between right/similar triangles algebraically using trigonometric ratios and relationships.

# Section 1: The Unit Circle and the Cosine and Sine Functions

In this module we will introduce and study the two basic trigonometric functions – **Cosine **and **Sine**. As we will see any point in the x-y plane is some (radial) distance ** r** away from the origin on a line through the origin. Since a line through the origin is inclined at some angle

**the coordinates of**

*θ***and**

*x***of any point in the plane can be written in terms**

*y***and cosine and sine of the angle**

*r***.**

*θ***Review: **Pythagorean Theorem for right angle triangles, positive and negative angles, radian and de**g**ree measures.

**Learning Objectives:**

- Equation of a circle of radius
and center (0,0e).*r* - Equation of the Unit Circle
- Reference angle
- Definition of Cosine and Sine
- Domain and Range of the Cosine and Sine Functions