TUC - Trigonometry and the Unit Circle Module Overview

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 Introduction

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Trigonometry finds its application in the unit circle, enabling us to solve real-world problems. In this module, we will build upon your knowledge of trigonometry (sine, cosine, and tangent) and establish connections with special right triangles and the coordinate plane. This unit presents an opportunity to integrate various mathematical concepts. I hope you are thrilled to embark on this journey.
     

Essential Questions

  • How do I think about an angle as the rotation of a ray around its endpoint?
  • What is meant by the radian measure of an angle?
  • What is the connection between the radian measure of an angle and the length of the arc on the unit circle the angle intercepts?

Introduction to Trigonometry Key Terms

The following key terms will help you understand the content in this module.

Coterminal Angles  - share the same initial side and the same terminal side of angles of rotation.

Initial Side - the "beginning" side of an angle of rotation, usually on the positive x-axis

Negative Angle - an angle in standard position is negative when the location of the terminal side results from a clockwise rotation

Positive Angle - an angle in standard position is positive when the location of the terminal side results from a counterclockwise rotation

Radian - the measure of the central angle of a circle subtended by an arc of equal length to the radius

Reference Angle - the measure of the acute angle formed by the terminal side and the x-axis

Standard Position - an angle is in standard position when the vertex is at the origin and the initial side lies on the positive x-axis

Terminal Side - the "ending" side of an angle of rotation

Unit Circle - a circle with a radius of 1 and center at the origin

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