Unit 3 – Trigonometric and Polar Functions – Pre Calculus

3.1 Periodic Phenomena

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AP Learning Objectives: 
3.1.A  Construct graphs of periodic relationships based on verbal representations.
3.2.B  Describe key characteristics of a periodic function based on a verbal representation.

3.2A Radians

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AP Learning Objectives: 
​3.2.A Determine the sine, cosine, and tangent of an angle using the unit circle.

3.2B Sine, Cosine, and Tangent

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AP Learning Objectives: 
3.2.A Determine the sine, cosine, and tangent of an angle using the unit circle.

 

3.3A Sine and Cosine Function Values

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AP Learning Objectives: 
3.3.A Determine coordinates of points on a circle centered at the origin.

3.3B Sine and Cosine Function Values

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AP Learning Objectives: 
3.3.A Determine coordinates of points on a circle centered at the origin.

3.4 Sine and Cosine Function Graphs

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AP Learning Objectives: 
3.4.A Construct representations of the sine and cosine functions using the unit circle.

3.5 Sinusoidal Functions

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AP Learning Objectives: 
3.5.A  Identify key characteristics of the sine and cosine functions.

3.6A Sinusoidal Function Transformations

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AP Learning Objectives: 
Lesson 3.6A focuses on amplitude, vertical shift, and period of a sinusoidal function. 
Lesson 3.6B focuses on phase shift of a sinusoidal function. 

3.6B Sinusoidal Function Transformations

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AP Learning Objectives: 
Lesson 3.6A focuses on amplitude, vertical shift, and period of a sinusoidal function. 
Lesson 3.6B focuses on phase shift of a sinusoidal function. 

3.7 Sinusoidal Function Context and Data Modeling

 

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AP Learning Objectives: 

Unit 3A Review

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3.8 The Tangent Function

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AP Learning Objectives: 
3.8.A  Construct representations of the tangent function using the unit circle.
3.8.B  Describe key characteristics of the tangent function.
​3.8.C  Describe additive and multiplicative transformations involving the tangent function.

3.9 Inverse Trigonometric Functions

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AP Learning Objectives:
3.9A  Construct analytical and graphical representations of the inverse of the sine, cosine, and tangent             functions over a restricted domain. 

3.10 Trigonometric Equations and Inequalities

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AP Learning Objectives: 
3.10.A Solve equations and inequalities involving trigonometric functions. 

3.11 Cosecant, Secant, Cotangent Functions

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AP Learning Objectives: 
3.11.A  Identify key characteristics of functions that involve quotients of the sine and cosine                functions. 

 

3.12A Equivalent Representations of Trigonometric Functions

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AP Learning Objectives: 
3.12.A  Rewrite trigonometric expressions in equivalent forms with the Pythagorean identity.
3.12.C  Solve equations using equivalent analytic representations of trigonometric functions.

3.12B Equivalent Representations of Trigonometric Functions

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BAP Learning Objectives: 
3.12.B  Rewrite trigonometric expressions in equivalent forms with the sine and cosine sum                 identities.
3.12.C  Solve equations using equivalent analytic representations of trigonometric functions.

3.13 Trigonometric and Polar Coordinates

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BAP Learning Objectives: 
3.13.A  Determine the location of a point in the plane using both rectangular and polar 
​             coordinates. 

3.14A Polar Function Graphs

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AP Learning Objectives: 
3.14.A  Construct Graphs of Polar Functions

3.14B Polar Function Graphs

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AP Learning Objectives: 
3.14.A  Construct Graphs of Polar Functions

3.15 Rates of Change in Polar Functions

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BAP Learning Objectives: 
3.15.A  Determine the characteristics of the graph of a polar function.

Unit 3B Review

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