Lesson 7.1: Calculus in Polar Coordinates

In this lesson, you will learn about slope of tangent lines, area of regions in polar coordinates, and arc length for polar curves.

View all of the instructional videos, read the provided readings, and practice exercises/activities. These will help you master the objectives for this lesson. Pay attention to additional comments provided. It helps to review basic concepts of polar coordinates and graphing polar curves.

Lesson Objectives

Upon completion of the lesson 7.1, you will be able to:

• Determine slopes of tangent lines

• Determine intersections of basic polar curves

• Determine area of regions bounded by polar curves

• Model and solve applications

Lesson Content

View all of the following instructional videos. These will help you master the objectives for this module.

1. Polar Coordinates – The Basics [10:34]

   1. Source: prickJMT

1. Slopes of Tangent Lines in Polar Form [2:10]

   1. Source: patrickJMT

   2. Example 1:

1. Example 2: [4:18]

1. Example 3: [3:18]

1. Finding Areas in Polar Coordinates [8:49]

   1. Source: patrickJMT

• 1. Horizontal and Vertical Tangent Lines to Polar Curves [11:00]

  2. Source: bullcleo1

• 1. Vertical and Horizontal Tangent Lines to the Polar Curve [10:36]

  2. Source: TheIntegralCALC

• 1. Something for you to think about: how do you know those are all the solutions?

  2. Points of Intersection of Two Polar Curves [13:12]

  3. Source: TheIntegralCALC

• 1. It helps to visualize the curves first.

  2. Area Bounded by Two Polar Curves [8:09]

  3. Source: bullcleo1

  4. Part 1:

• 1. Part 2: [7:53]

• • 1. When you present your solution, you must not mix definition integral and indefinite integral. Either you change the limits of integration after the u-sub or you find the antiderivative first then integrate the definite integral.

Lesson Readings

The following required readings cover the content for this module. As you go through each reading, pay close attention to the content that will help you learn the objectives for this module.

1. Polar Coordinates

2. Paul’s Online Math Notes

3. Area of Regions in Polar Coordinates (Sect. 11.5)

4. Areas and Lengths in Polar Coordinates

5. Area with Polar Coordinates

6. Paul’s Online Math Notes

7. Arc Length with Polar Coordinates

8. Paul’s Online Math Notes

9. Arc Length in Polar Coordinates

Lesson Practice Exercises/Activities

Make your way through each of the practice exercises. This is where you will take what you have learned from the lesson content and lesson readings and apply it by solving practice problems.

1. Area and Arch Length in Polar Coordinates

2. Polar Coordinates

3. Area Bounded by a Polar Curve

4. David P. Little

Additional Resources

Below are additional resources that help reinforce the content for this module.

1. Arc Length of a Curve (see Polar)

2. www.mathwords.com

3. Area and Arc Length in Polar Coordinates

4. eCourses

5. 10.4: Areas and Lengths in Polar Coordinates

6. Finding Area Bounded by Two Polar Curves (video) [14:53]

7. Source: patrickJMT

1. Areas Bounded by Two Polar Curves – Another Ex 2 (video) [5:33]

2. Source: patrickJMT

Homework Assignments

Do Homework 7.1 on MyMathLab

Show Your Work Assignment

Show Your Work assignment will be given via Assignment Tool on Laulima. Please check your email for Laulima announcement.

Start Lesson 7.2: Conic Section -->