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
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:
Skills You Will Master
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