Polar Coordinates and Graphs (BC Calculus – Unit 9)

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Description

Polar Coordinates and Graphs Lesson:
Your AP Calculus BC students will find slope of a tangent line to a polar graph, apply definite integrals to polar form problems and sketch graphs in polar form.

What is included in this resource?

⭐ Guided Student Notes

⭐ Fully-editable SMART Board® Slides

⭐ Homework/Practice assignment

⭐ Content quiz

⭐ Video Lesson Link for Distance Learning – Flipped Classroom models

⭐ Full solution set

***(2/17/2023) Added equation to Form B Daily Quiz Student copy

Lesson Objective:

★ Use the polar coordinate system to convert rectangular coordinates and equations into polar form and vice versa.

★ Sketch the graph of an equation in polar form.

★ Find the slope of a tangent line to a polar graph.

★ Apply definite integrals to polar form problems.

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NOTE: This lesson has been updated to reflect the changes in the AP Calculus CED Binder .

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College Board® Topics:

Topic 9.7: Defining Polar Coordinates and Differentiation in Polar Form

College Board® Learning Objectives:

FUN-3.G: Calculate derivatives of functions written in polar coordinates. BC ONLY

FUN-3.G.1: Methods for calculating derivatives of real-valued functions can be extended to functions in polar coordinates. BC ONLY

FUN-3.G.2: For a curve given by a polar equation r=f(θ), derivatives of r, x, and y with respect to θ, and first and second derivatives of y with respect to x can provide information about the curve. BC ONLY

The unit includes the following topics:

1. Parametric Equations and Calculus

2. Parametric Equations and Arc Length

4. Velocity and Acceleration of Vector Functions

5. Polar Coordinates and Graphs

6. Area and Arc Length in Polar Coordinates

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