Subject:
Mathematics
Material Type:
Module
Provider:
Ohio Open Ed Collaborative
Tags:
Mathematics, Tmm0022
Language:
English
Media Formats:
Text/HTML

# The Unit Circle and Cosine and Sine Functions

## 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.*

• 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.

# 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 θ the coordinates  of x and y  of any point in the plane can be written in terms r  and cosine and sine of the angle θ.

Review: Pythagorean Theorem for right angle triangles, positive and negative angles, radian and degree measures.

Learning Objectives:

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