Unit 5 — Trigonometric Functions

Unit 5 · Trigonometric Functions

Trigonometric Functions

Build the trigonometric foundation — angles in standard position, the unit circle, all six trig functions, and right triangle applications — that every later trig unit depends on.

Estimated Time

2–3 weeks

Difficulty

Intermediate

4 Lessons
5 Learning Goals
13 Vocabulary Terms

Overview

Unit description, learning objectives, and skills.

Unit 5 — Trigonometric Functions is the entry point to trigonometry. You will learn to measure angles in radians, navigate the unit circle, evaluate all six trig functions at standard angles, and apply right triangle trigonometry to real-world problems involving angles of elevation and depression.

Learning Objectives

By the end of this unit, you will be able to:

Goal 1Convert between degree and radian measure and find coterminal angles.
Goal 2Define sine and cosine using the unit circle and evaluate them at standard angles.
Goal 3Define and evaluate all six trigonometric functions using the unit circle and reference angles.
Goal 4Apply right triangle trigonometry to find missing sides and angles.
Goal 5Solve right triangle application problems involving angles of elevation and depression.

Skills You Will Master

Angles & radian measure
Unit circle & standard angles
All six trig functions
Right triangle trigonometry
Elevation & depression applications

Real-World Connection

Trigonometry is the mathematics of angles and cycles. Surveyors use angles of elevation and depression to measure heights of buildings and mountains without climbing them. Architects use right triangle trig to calculate roof pitches and structural loads. Navigation — from ancient sailors using the stars to modern GPS — relies on trigonometric calculations. The unit circle is also the foundation of wave analysis, which describes sound, light, and electrical signals. Every oscillating system in nature is modeled with the functions you learn in Unit 5.

Chapter Checklist

Recommended steps for completing each chapter

  • Read the Workbook
  • Complete the Independent Study
  • Finish the Exit Ticket
  • Take the Quiz
  • Review the Answer Key
  • Continue to the Next Chapter