In this lesson, you will learn about polar coordinates by their basic definitions, determining points in polar coordinates, basic curves, and graphing them.
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. Review trigonometric identities and special values if necessary. The angle in the polar coordinate is expressed in radians, although in practice it sometimes is expressed in degrees. (For example, a simple polar equation, r=θ, does not make sense if we allow θ to be in degrees, since |r| represents the distance between the point and the pole, it cannot be in degrees). Polar representation of a point is not unique. When you covert the given rectangular coordinates of a point to polar coordinates, it is very helpful to first visualize the position of the point, which helps to determine the angle θ (calculator may not be able to give the answer that you are looking for directly, because the ranges of inverse trigonometric functions). In some cases, if you visualize the point first in the Cartesian plane, you may even be able to write out the polar coordinates without any computation.
Upon completion of the lesson 5.1, you will be able to:
Identify and plot points along with simple polar curves
Convert between Cartesian coordinates and polar coordinates
View all of the following instructional videos. These will help you master the objectives for this module.
Precalculus – Introduction to Polar Coordinate [3:33]
Source: brightstorm2 from YouTube
Precalculus – Converting from Polar Coordinates to Rectangular [4:42]
Source: brightstorm2 from YouTube
Note: The presenter got the title of the video wrong. It should have been "Converting from Rectangular to Polar Coordinates." The presenter uses both sine function and cosine function to determine the value of θ instead of using the tangent function, which is fine. Remember: before determine the value of θ, visualize where the point is in the Cartesian plane.
Polar Coordinates – Basics [10:34]
Source: patrickJMT from YouTube
Polar Coordinates - The Basics are discussed. It shows how to graph a 'polar point' as well as how to convert from Cartesian to polar form and vice-versa.
Graphing a Polar Curve – Part 1 [6:57]
Source: patrickJMT from YouTube
In this video, it discusses how to graph the polar curve
r=3cos(2θ). If you are asked to graph a polar curve by hand, usually you will need to find a few more point (by using a calculator) to help you to shape the curve. For example, instead of using only two values of θ, 0 and π4, for the first piece, you may want to find a few more points in between, say find the values of r when θ is π12, π8 and π6. Also you may want to use the facts that cosine function is even and is periodic.
Graphing a Polar Curve – Part 2 [2:39]
Source: patrickJMT from YouTube
Graphing Polar Equations I [8:11]
Source: bullcleo1 from YouTube
Polar equations for circles.
Converting Polar Equations to Rectangular Equations [7:27]
Source: bullcleo1 from YouTube
Can you think of an easier way to solve the last example?
Special Polar Graphs [6:11]
Source: fractad from YouTube
Difference Between Cartesian and Polar Coordinates (animation Only) [1:34]
Source: Psyvrcharticgrsheltu from YouTube
Cool Polar Graph (interval 0≤θ≤10π) (animation only) [0:46]
Source: Psyvrcharticgrsheltu from YouTube
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.
Paul’s Online Math Notes
MathisFun.com
Read with caution.
by Elmer Nocon, Angelo Bernable, and Mark Kenneth Hitosis
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.
17Calculus
Practice problems with solutions. Additional links to videos at the bottom of the page also which may be helpful.
Below are additional resources that help reinforce the content for this module.
Online conversion tool to check your work (has a mobile view option to view and use on a cellular device, they have apps as well).
Another free help site. Like MathNerds, they won't just do your homework for you!
Do Homework 5.1 on MyMathLab.
Show Your Work assignment will be given via Assignment Tool on Laulima. Please check your email for Laulima announcement.