Student Resources

UNIT V: Parametric Equations and Polar Coordinate System

Activities

1 Parametric, Vector, Polar and 3-D functions
In this TI activity, students investigate and graph parametric functions, vectors, polar functions, and 3D functions.
2 Parametric, Polar, and 3-D Functions
In this TI activity, students investigate and graph parametric functions, vectors, polar functions, and 3D functions.
3 Parametric, Vector, Polar and 3-D functions
In this TI activity, students investigate and graph parametric functions, vectors, polar functions, and 3D functions.

eTools

4 Area Inside a Polar Curve
Interactive applet that allows the user to visualize sweeping out the area inside a polar curve.
5 Famous Polar Curves
List of applets that allow the user to explore famous polar curves.
6 Graphing Cycloids (Applet: Cycloids)
By adjusting the length of the radius, the user can produce the graphs of various types of cycloids.
7 Parametric Equations in Three Dimensions
Graphs a path in three-dimensions.
8 Plotting Polar Points (Applet: Polar Coordinates)
This applet allows the user to drag a point in the polar coordinate system and note the changes to r, theta, x, and y. The coordinate grid lines may be turned on or off.

Reviews

9 Polar Coordinates and Graphing
AP-style problems.

Teacher Support

10 The Cycloid Family

Text

11 Larson 6th Edition, Section 9.2
12 Larson 6th Edition, Section 9.2
13 Larson 6th Edition, Section 9.2
D
14 Larson 6th Edition, Section 9.3
15 Larson 6th Edition, Section 9.3
16 Larson 6th Edition, Section 9.4
17 Larson 6th Edition, Section 9.4
18 Larson 6th Edition, Section 9.4
19 Larson 6th Edition, Section 9.4
20 Larson 6th Edition, Section 9.5
21 Larson 6th Edition, Section 9.5
22 Pearson 3rd Edition, Section 10.1
23 Pearson 3rd Edition, Section 10.1
24 Pearson 3rd Edition, Section 10.1
25 Pearson 3rd Edition, Section 10.1
26 Pearson 3rd Edition, Section 10.1
27 Pearson 3rd Edition, Section 10.3
28 Pearson 3rd Edition, Section 10.3
29 Pearson 3rd Edition, Section 10.3
30 Pearson 3rd Edition, Section 10.3

Tutorials

31 Parametric Derivatives
This is a tutorial fro finding parametric derivatives.
32 Parametric Integrals
This tutorial demonstrates how to evaluate parametric integrals.
33 Polar Coordinates
The first segment of this online tutorial provides an introduction to polar coordinates.
34 Polar Coordinates (Calculus Book II, Chapter 5, Section 2)
Tutorial includes extensive notes (if you click on the Help button) and step-by-step interactive problems.
35 Polar Graphs
Section 3 of this link provides an online tutorial for sketching polar graphs.
36 Polar Integrals
This tutorial demonstrates how to evaluate polar integrals.
37 Sketching Polar Curves (Calculus Book II, Chapter 5, Section 2, Module 3)
Tutorial includes extensive notes (if you click on the Help button) and step-by-step interactive problems.

UNIT VI: Vectors

eTools

1 Graphical Respresentation of Cross Product
This applet allows the user to drag a vector in a plane and view the resulting cross product vector.
2 Graphing Vectors in Three Dimensions
This applet allows the user to enter coordinates to create vectors, and the "boxes" created by the endpoints.
3 Interactive Gallery of Quadric Surfaces
This online resource provides an interactive gallery of quadric surfaces.
4 Linear Combinations in 3-D
This link contains an applet that allows the user to insert vectors and graph linear combinations.
5 Relations between Cartesian, Cylindrical, and Spherical Coordinates
This online resource explains how to convert between cartesian, cylindrical, and spherical coordinates.

Reviews

6 Converting Coordinates
This link reviews how to change cylindrical coordinates into rectangular coordinates.
7 Shortest Distances
This link reviews shortest distances between a point and a plane.
8 Surfaces of Revolution
This link contains equations for surfaces of revolution and 3-D graphs.

Text

9 Larson 6th Edition, Section 10.1
10 Larson 6th Edition, Section 10.1
11 Larson 6th Edition, Section 10.1
12 Larson 6th Edition, Section 10.2
13 Larson 6th Edition, Section 10.2
14 Larson 6th Edition, Section 10.2
15 Larson 6th Edition, Section 10.3
16 Larson 6th Edition, Section 10.3
17 Larson 6th Edition, Section 10.3
18 Larson 6th Edition, Section 10.3
19 Larson 6th Edition, Section 10.4
20 Larson 6th Edition, Section 10.5
21 Larson 6th Edition, Section 10.5
22 Larson 6th Edition, Section 10.5
23 Larson 6th Edition, Section 10.6
24 Larson 6th Edition, Section 10.6
25 Larson 6th Edition, Section 10.7
26 Larson 6th Edition, Section 10.7
27 Pearson 3rd Edition, Section 10.2
28 Pearson 3rd Edition, Section 11.1
29 Pearson 3rd Edition, Section 11.1
30 Pearson 3rd Edition, Section 11.1
31 Pearson 3rd Edition, Section 11.1
32 Pearson 3rd Edition, Section 11.1
33 Pearson 3rd Edition, Section 11.2
34 Pearson 3rd Edition, Section 11.2
35 Pearson 3rd Edition, Section 11.2
36 Pearson 3rd Edition, Section 11.2
37 Pearson 3rd Edition, Section 11.3
38 Pearson 3rd Edition, Section 11.4
39 Pearson 3rd Edition, Section 11.4
40 Pearson 3rd Edition, Section 11.4
41 Pearson 3rd Edition, Section 11.5
42 Pearson 3rd Edition, Section 11.5, 14.6
43 Pearson 3rd Edition, Section 11.5, 14.6
44 Pearson 3rd Edition, Section 11.6

Tutorials

45 Cross Product (Calculus Book III, Chapter 2, Section 4)
Tutorial includes extensive notes (if you click on the Help button) and step-by-step interactive problems.
46 Dot Product (Calculus Book III, Chapter 2, Sections 2-3)
Tutorial includes extensive notes (if you click on the Help button) and step-by-step interactive problems.
47 Dot Product (Calculus Book III, Chapter 2, Sections 2-3)
Tutorial includes extensive notes (if you click on the Help button) and step-by-step interactive problems.
48 Equations of Lines in Space (Calculus Book III, Chapter 2, Section 5, Module 1)
Tutorial includes extensive notes (if you click on the Help button) and step-by-step interactive problems.
49 Equations of Planes (Calculus Book III, Chapter 2, Section 5, Module 2)
Tutorial includes extensive notes (if you click on the Help button) and step-by-step interactive problems.
50 Introduction to Vectors
This link provides an online tutorial introduction to vectors.
51 Orthogonal Vectors (Calculus Book III, Chapter 2, Section 2, Module 5)
Tutorial includes extensive notes (if you click on the Help button) and step-by-step interactive problems.
52 Unit Vectors
This link provides an online tutorial for an introduction to unit vectors.
53 Vector Projection (Calculus Book III, Chapter 2, Section 2, Module 4)
Tutorial includes extensive notes (if you click on the Help button) and step-by-step interactive problems.
54 Vectors (Calculus Book III, Chapter 2, Section 1)
Tutorial includes extensive notes (if you click on the Help button) and step-by-step interactive problems.