Lesson 4: 10.4 Areas and Lengths in Polar Coordinates
Duration of Days: 2
Lesson Objective
Students will be able to apply previously learned calculus concepts (slopes of tangent lines, areas of enclosed sections of a graph, and arc lengths) to polar graphs.
- What will we need to adjust in our calculus formulas to accomodate polar graphs?
(no new terminology)
(applying calculus concepts to polar graphs)
- Apply calculus concepts (slope of a tangent line, area, and arc length) to polar curves
- DOK Levels 1-4
- detecting, tracking, and locating objects with sonar or radar
- modeling how microphones capture sound
- In aviation and maritime transport, positions are defined by bearing (angle) and distance from a reference point
- Celestial bodies (planets, satellites) follow orbits and paths calculated using polar equations to describe their motion and position over time
Calculating endpoints of integration for an enclosed area can sometimes be confusing for students. Intersection points can be more difficult to conceptualize when the independent variable is an angle.
Homogeneous grouping and whole-class discussion
section assessment
problems assigned from book