Download ArticleDownload ArticleThis article was co-authored by Taylor Klein. Taylor Klein is an Advanced Math Teacher based in Philadelphia, Pennsylvania. She has worked in the education field for over 10 years, including eight years as a middle school Advanced Math Teacher. She has a master’s degree in Instructional Technology and Design and a master’s degree in Educational Leadership and Administration.
This article has been fact-checked, ensuring the accuracy of any cited facts and confirming the authority of its sources.
This article has been viewed 88,292 times.
Polar functions are functions of the form r = f(θ). While you can make some really cool graphs with them, they are really quite tricky to work with.[1]
Steps
Download Article
Understand how polar equations work. Coordinates in polar equations are of the form (r,θ), where r represents radius and θ represents angle. This means you rotate θ radians around and go out r units.[2]
Make a table with values of the angle and radius. Take any random values of θ (around ten values would suffice) and calculate r against each of them using the relationship given between r and θ. This will help you plot them out on a graph easier, because you can just refer to a table instead of having to come up with coordinates in your head.[3]Advertisement
Plot the various (r,θ) points as found in the table.[4]
The How.com.vn How to Plot Polar Coordinates will be helpful.
Join the plotted points with a smooth curve and you're done![5]EXPERT TIPJoseph Meyer is a High School Math Teacher based in Pittsburgh, Pennsylvania. He is an educator at City Charter High School, where he has been teaching for over 7 years. Joseph is also the founder of Sandbox Math, an online learning community dedicated to helping students succeed in Algebra. His site is set apart by its focus on fostering genuine comprehension through step-by-step understanding (instead of just getting the correct final answer), enabling learners to identify and overcome misunderstandings and confidently take on any test they face. He received his MA in Physics from Case Western Reserve University and his BA in Physics from Baldwin Wallace University.Math Teacher
Joseph Meyer
Math TeacherDevelop strong graphing skills. Drawing graphs by hand will help you develop foundational graphing skills, especially in understanding scales and axes. This will build a strong base for you to use helpful online tools to visualize complex relationships, perform calculations, and prepare for standardized tests.
Expert Q&A
- QuestionHow do I graph equations?
Taylor KleinTaylor Klein is an Advanced Math Teacher based in Philadelphia, Pennsylvania. She has worked in the education field for over 10 years, including eight years as a middle school Advanced Math Teacher. She has a master’s degree in Instructional Technology and Design and a master’s degree in Educational Leadership and Administration.
Advanced Math TeacherWhen graphing an equation, start by ensuring the equation is in a suitable form. In the case of the slope-intercept form (Y = MX + B), recognize that B represents the Y-intercept, serving as the starting point. Plot the first point on the Y-intercept, and then determine the slope (M), where slope equals rise over run. In standard form, finding X and Y intercepts is an effective approach, achieved by creating an X-Y input-output table. Finally, for point-slope form, understand that the slope is outside the parentheses, while the points are the inverse of what's inside the parentheses, aiding in a comprehensive understanding of graphing equations. - QuestionHow do I graph r = 2 + 3cos theta?
Community AnswerMake a theta and r table. Plug in various values of theta. Lastly, graph on polar graph paper. - QuestionHow do I graph 1 - 3 sin theta?
DonaganTop AnswererLet one of the axes (say, the x-axis) show the values of theta (Θ) from 0° to 90° (or higher). Let the other axis (y) show the values of the function (1 - 3 sin Θ). Construct a table of values pairing each theta value with its respective function value. Then plot the graph as you would with x and y values. You'll need a trig table for the sine values.
Video
Tips
- Make sure the angle is in radians.Thanks
- Using special graph paper designed specifically for polar equations will make this a lot easier.Thanks
- You can also use a graphing calculator to do this a lot easier, and more accurately.Thanks
Warnings
- If you graph this by hand, making θ's interval too large will result in an inaccurate graph. Try to choose an interval that won't be too inaccurate but won't be too time consuming to graph.Thanks
Expert Interview
Thanks for reading our article! If you’d like to learn more about mathematics, check out our in-depth interview with Taylor Klein.
References
- ↑ https://www.khanacademy.org/math/ap-calculus-bc/bc-advanced-functions-new/bc-9-7/v/derivatives-in-polar-coordinates
- ↑ https://courses.lumenlearning.com/boundless-algebra/chapter/the-polar-coordinate-system/
- ↑ https://openstax.org/books/calculus-volume-2/pages/7-3-polar-coordinates
- ↑ https://www.ck12.org/book/ck-12-trigonometry-second-edition/section/6.2/
- ↑ https://www.alamo.edu/contentassets/35e1aad11a064ee2ae161ba2ae3b2559/additional/math2412-graphs-polar-equations.pdf
About This Article
Did this article help you?
⚠️ Disclaimer:
Content from Wiki How English language website. Text is available under the Creative Commons Attribution-Share Alike License; additional terms may apply.
Wiki How does not encourage the violation of any laws, and cannot be responsible for any violations of such laws, should you link to this domain, or use, reproduce, or republish the information contained herein.
- - A few of these subjects are frequently censored by educational, governmental, corporate, parental and other filtering schemes.
- - Some articles may contain names, images, artworks or descriptions of events that some cultures restrict access to
- - Please note: Wiki How does not give you opinion about the law, or advice about medical. If you need specific advice (for example, medical, legal, financial or risk management), please seek a professional who is licensed or knowledgeable in that area.
- - Readers should not judge the importance of topics based on their coverage on Wiki How, nor think a topic is important just because it is the subject of a Wiki article.
