Unit 6 — Periodic Functions

Unit 6 · Periodic Functions

Periodic Functions

Graph and analyze the six trigonometric functions — amplitude, period, phase shift, and vertical shift — and find inverse trig values for solving equations.

Estimated Time

2–3 weeks

Difficulty

Intermediate

3 Lessons
5 Learning Goals
10 Vocabulary Terms

Overview

Unit description, learning objectives, and skills.

Unit 6 — Periodic Functions brings the unit circle to life on the coordinate plane. You will graph sine and cosine with full control over amplitude, period, phase shift, and vertical shift, then extend to the other four trig functions. The unit closes with inverse trig functions — the tools for working backwards from a ratio to an angle.

Learning Objectives

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

Goal 1Graph sine and cosine functions, identifying amplitude, period, phase shift, and vertical shift.
Goal 2Write equations of sine and cosine functions from their graphs.
Goal 3Graph tangent, cotangent, secant, and cosecant functions and identify their asymptotes.
Goal 4Evaluate inverse trigonometric functions and interpret their restricted domains.
Goal 5Compose trigonometric and inverse trigonometric functions to simplify expressions.

Skills You Will Master

Graphing sine & cosine
Amplitude, period & shifts
Graphing tan, cot, sec, csc
Inverse trig functions

Real-World Connection

Periodic functions are the language of waves. Sound engineers use amplitude and period to describe audio signals. Electrical engineers use sine waves to model alternating current. Oceanographers use periodic functions to model tides. Physicians use them to analyze EKG waveforms. Whenever a physical quantity oscillates — a pendulum, a spring, a radio signal — a sine or cosine function describes it exactly. The inverse trig functions let you work backwards: given a measurement, find the angle or phase that produced it.

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