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.
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 PhenomenaTo 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.
Periodic Phenomena
Periodic Phenomena
- What a Periodic Function Is
- Recognizing Periodicity and Finding the Period
- Graphing from One Cycle
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
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
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
Sinusoidal Functions
Sinusoidal Functions
- What Sinusoidal Functions Are
- The Key Characteristics of a Sinusoidal Graph
- How to Read These Characteristics from a Graph
Sinusoidal Function Transformations
Sinusoidal Function Transformations
- What Sinusoidal Transformations Are
- Reading the Parameters from an Equation
- Sketching One Cycle from the Equation
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
The Tangent Function
The Tangent Function
- What Tangent Is
- The Parent Tangent Graph
- Transformations of Tangent
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
Trigonometric Equations and Inequalities
Trigonometric Equations and Inequalities
- Solving Trigonometric Equations
- Solving on an Interval and with Transformed Angles
- Trigonometric Inequalities
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
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
Trigonometry and Polar Coordinates
Trigonometry and Polar Coordinates
- What Polar Coordinates Are
- Equivalent Polar Representations
- Converting Between Polar and Rectangular Coordinates
Polar Function Graphs
Polar Function Graphs
- What a Polar Function Graph Is
- How to Construct the Graph
- Restricted Domains and Endpoints
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
Notes
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