AP®︎ Precalculus Unit 3: Notes & Study Guide

Prepare for your quiz, test, or the AP exam with a comprehensive review on Unit 3 of AP Precalculus – Trigonometric and Polar Functions.

Exam weight: 30-35%
15 Topics

Unit 3: Trigonometric and Polar Functions

This unit examines trigonometric functions and polar coordinates to model periodic behavior and relationships involving angles and rotation.

Begin with Topic 3.1: Periodic Phenomena

To review Unit 3, go through each of the 15 topics below.

Everything you actually need to know for your Unit 3 test, pulled directly from the AP® Precalculus curriculum.

Topic 3.1
~6 min
Review
Periodic Phenomena
Periodic Phenomena
  • What a Periodic Function Is
  • Recognizing Periodicity and Finding the Period
  • Graphing from One Cycle
Review
Topic 3.2
~5 min
Review
Sine, Cosine, and Tangent
Sine, Cosine, and Tangent
  • Sine, Cosine, and Tangent on the Unit Circle
  • Standard Position, Radians, and Coterminal Angles
  • Finding Trig Values from a Point or Ray
Review
Topic 3.3
~5 min
Review
Sine and Cosine Function Values
Sine and Cosine Function Values
  • Sine and Cosine as Circle Coordinates
  • Exact Values You Need to Know
  • Quadrants, Reference Angles, and Coterminal Angles
Review
Topic 3.4
~5 min
Review
Sine and Cosine Function Graphs
Sine and Cosine Function Graphs
  • What Sine and Cosine Are
  • Building the Parent Graphs from the Unit Circle
  • Reading Key Features from the Circle and the Graph
Review
Topic 3.5
~6 min
Review
Sinusoidal Functions
Sinusoidal Functions
  • What Sinusoidal Functions Are
  • The Key Characteristics of a Sinusoidal Graph
  • How to Read These Characteristics from a Graph
Review
Topic 3.6
~5 min
Review
Sinusoidal Function Transformations
Sinusoidal Function Transformations
  • What Sinusoidal Transformations Are
  • Reading the Parameters from an Equation
  • Sketching One Cycle from the Equation
Review
Topic 3.7
~6 min
Review
Sinusoidal Function Context and Data Modeling
Sinusoidal Function Context and Data Modeling
  • What a Sinusoidal Model Is
  • Building the Model from Context, a Graph, or a Table
  • Sinusoidal Regression and Reading the Output
Review
Topic 3.8
~5 min
Review
The Tangent Function
The Tangent Function
  • What Tangent Is
  • The Parent Tangent Graph
  • Transformations of Tangent
Review
Topic 3.9
~5 min
Review
Inverse Trigonometric Functions
Inverse Trigonometric Functions
  • Restricted domains that make trig invertible
  • The Three Inverse Trig Functions and Their Restricted Domains
  • Constructing the Inverse Analytically and Graphically
Review
Topic 3.10
~6 min
Review
Trigonometric Equations and Inequalities
Trigonometric Equations and Inequalities
  • Solving Trigonometric Equations
  • Solving on an Interval and with Transformed Angles
  • Trigonometric Inequalities
Review
Topic 3.11
~5 min
Review
The Secant, Cosecant, and Cotangent Functions
The Secant, Cosecant, and Cotangent Functions
  • What Secant, Cosecant, and Cotangent Are
  • Key Characteristics of the Three Graphs
  • Finding Values and Graphing from Sine and Cosine
Review
Topic 3.12
~5 min
Review
Equivalent Representations of Trigonometric Functions
Equivalent Representations of Trigonometric Functions
  • What Equivalent Trigonometric Forms Are
  • Identities You Should Be Ready to Generate and Use
  • Choosing the Best Rewrite
Review
Topic 3.13
~5 min
Review
Trigonometry and Polar Coordinates
Trigonometry and Polar Coordinates
  • What Polar Coordinates Are
  • Equivalent Polar Representations
  • Converting Between Polar and Rectangular Coordinates
Review
Topic 3.14
~6 min
Review
Polar Function Graphs
Polar Function Graphs
  • What a Polar Function Graph Is
  • How to Construct the Graph
  • Restricted Domains and Endpoints
Review
Topic 3.15
~6 min
Review
Rates of Change in Polar Functions
Rates of Change in Polar Functions
  • Signed Radius and Distance from the Origin
  • Reading Radial Behavior from a Formula, Table, or Graph
  • Closest and Farthest Points from Relative Extrema
Review

Notes

1 credit used · 5/5 remaining