<center> [](https://3speak.tv/watch?v=mes/rmcyoeql) ▶️ [Watch on 3Speak](https://3speak.tv/watch?v=mes/rmcyoeql) </center> --- In this video I go three interesting and useful symmetry properties of polar coordinate functions, which can be used to save time in sketching polar curves. The first property is that if we can replace ϴ by -ϴ and the function remains the same than what we have is a function that is symmetric about the polar axis. The second property is that if the function r is replaced by -r still obtains the same function, than we have is a function symmetric about origin or pole. In other words, we can rotate the function by an angle of π radians and still obtain the same function. The third property is when we replace the angle ϴ with π - ϴ and still update the same function; this means that the curve is symmetric about the angle π/2 radians or 90 degrees. Also in this video I show how we could have used these properties to save time in graphing the curves from my earlier videos on Examples 6, 7, and 8. This is because those examples involved graphing curves that were indeed symmetric by at least one of the above properties. This is a very extensive and detailed video illustrating how to use symmetry in polar coordinates to sketch curves, so make sure to watch this video! Download the notes in my video: https://1drv.ms/b/s!As32ynv0LoaIhvMD59uarZ1ut0semw View video notes on the Hive blockchain: https://peakd.com/@mes/video-notes-polar-coordinates-symmetry Related Videos: Polar Coordinates: Example 8: Four-Leaved Rose: [https://youtu.be/mTk5j0jD3dE](https://youtu.be/mTk5j0jD3dE) Polar Coordinates: Example 7: Cardioid: [https://youtu.be/rPErcaqNUIY](https://youtu.be/rPErcaqNUIY) Polar Coordinates: Example 6: Part 2: Polar Circle to Cartesian: [https://youtu.be/biUHN-BphkE](https://youtu.be/biUHN-BphkE) Polar Coordinates: Example 5: Straight Lines: [https://youtu.be/AGSz3EVi05A](https://youtu.be/AGSz3EVi05A) Polar Coordinates: Example 4: Circle: [https://youtu.be/ebsaIlXaZxs](https://youtu.be/ebsaIlXaZxs) Polar Coordinates: Example 3: Cartesian to Polar: [https://youtu.be/mV-9KTQM-RU](https://youtu.be/mV-9KTQM-RU) Polar Coordinates: Example 2: Polar to Cartesian: [https://youtu.be/mvpb9QshNNU](https://youtu.be/mvpb9QshNNU) Polar Coordinates: Cartesian Connection: [https://youtu.be/HcaTYrpmGaU](https://youtu.be/HcaTYrpmGaU) Polar Coordinates: Example 1: [https://youtu.be/q_kpqPpoLqE](https://youtu.be/q_kpqPpoLqE) Polar Coordinates: [https://youtu.be/-KAdZL-N4ok](https://youtu.be/-KAdZL-N4ok) Parametric Equations and Polar Coordinates: [https://youtu.be/usSors49Gdw](https://youtu.be/usSors49Gdw) Equation of a Circle and it's proof: [http://youtu.be/xMXYJ9UeF4I](http://youtu.be/xMXYJ9UeF4I) . ------------------------------------------------------ SUBSCRIBE via EMAIL: https://mes.fm/subscribe DONATE! ʕ •ᴥ•ʔ https://mes.fm/donate Like, Subscribe, Favorite, and Comment Below! Follow us on: MES Truth: https://mes.fm/truth Official Website: https://MES.fm Hive: https://peakd.com/@mes MORE Links: https://linktr.ee/matheasy Email me: contact@mes.fm Free Calculators: https://mes.fm/calculators BMI Calculator: https://bmicalculator.mes.fm Grade Calculator: https://gradecalculator.mes.fm Mortgage Calculator: https://mortgagecalculator.mes.fm Percentage Calculator: https://percentagecalculator.mes.fm Free Online Tools: https://mes.fm/tools iPhone and Android Apps: https://mes.fm/mobile-apps --- ▶️ [3Speak](https://3speak.tv/watch?v=mes/rmcyoeql)
| author | mes | ||||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| permlink | rmcyoeql | ||||||||||||
| category | hive-181335 | ||||||||||||
| json_metadata | "{"tags":["mathematics","calculus","science","stemgeeks","palnet","proofofbrain","education","stem","math"],"app":"3speak/0.3.0","type":"3speak/video","image":["https://ipfs-3speak.b-cdn.net/ipfs/bafybeiawd6egimrsfdmzieihsdtgnthhzz777dc7dssdkhcxzpfua4vkl4"],"video":{"info":{"platform":"3speak","title":"Polar Coordinates: Symmetry","author":"mes","permlink":"rmcyoeql","duration":1090.50195,"filesize":69599404,"file":"rsGAbQVlaCxBYppJLiTkjtyjyGCUKslpOKhoTSWkDIDhDpewIolNAHMDVidnWzMT.mp4","lang":"en","firstUpload":false,"ipfs":null,"ipfsThumbnail":null,"sourceMap":[{"type":"thumbnail","url":"ipfs://bafybeiawd6egimrsfdmzieihsdtgnthhzz777dc7dssdkhcxzpfua4vkl4"}]},"content":{"description":"In this video I go three interesting and useful symmetry properties of polar coordinate functions, which can be used to save time in sketching polar curves. The first property is that if we can replace ϴ by -ϴ and the function remains the same than what we have is a function that is symmetric about the polar axis. The second property is that if the function r is replaced by -r still obtains the same function, than we have is a function symmetric about origin or pole. In other words, we can rotate the function by an angle of π radians and still obtain the same function. The third property is when we replace the angle ϴ with π - ϴ and still update the same function; this means that the curve is symmetric about the angle π/2 radians or 90 degrees.\r\n\r\nAlso in this video I show how we could have used these properties to save time in graphing the curves from my earlier videos on Examples 6, 7, and 8. This is because those examples involved graphing curves that were indeed symmetric by at least one of the above properties.\r\n\r\nThis is a very extensive and detailed video illustrating how to use symmetry in polar coordinates to sketch curves, so make sure to watch this video!\r\n\r\nDownload the notes in my video: https://1drv.ms/b/s!As32ynv0LoaIhvMD59uarZ1ut0semw\r\n\r\nView video notes on the Hive blockchain: https://peakd.com/@mes/video-notes-polar-coordinates-symmetry\r\n\r\nRelated Videos: \r\n\r\nPolar Coordinates: Example 8: Four-Leaved Rose: [https://youtu.be/mTk5j0jD3dE](https://youtu.be/mTk5j0jD3dE)\r\nPolar Coordinates: Example 7: Cardioid: [https://youtu.be/rPErcaqNUIY](https://youtu.be/rPErcaqNUIY)\r\nPolar Coordinates: Example 6: Part 2: Polar Circle to Cartesian: [https://youtu.be/biUHN-BphkE](https://youtu.be/biUHN-BphkE)\r\nPolar Coordinates: Example 5: Straight Lines: [https://youtu.be/AGSz3EVi05A](https://youtu.be/AGSz3EVi05A)\r\nPolar Coordinates: Example 4: Circle: [https://youtu.be/ebsaIlXaZxs](https://youtu.be/ebsaIlXaZxs)\r\nPolar Coordinates: Example 3: Cartesian to Polar: [https://youtu.be/mV-9KTQM-RU](https://youtu.be/mV-9KTQM-RU)\r\nPolar Coordinates: Example 2: Polar to Cartesian: [https://youtu.be/mvpb9QshNNU](https://youtu.be/mvpb9QshNNU)\r\nPolar Coordinates: Cartesian Connection: [https://youtu.be/HcaTYrpmGaU](https://youtu.be/HcaTYrpmGaU)\r\nPolar Coordinates: Example 1: [https://youtu.be/q_kpqPpoLqE](https://youtu.be/q_kpqPpoLqE)\r\nPolar Coordinates: [https://youtu.be/-KAdZL-N4ok](https://youtu.be/-KAdZL-N4ok)\r\nParametric Equations and Polar Coordinates: [https://youtu.be/usSors49Gdw](https://youtu.be/usSors49Gdw)\r\nEquation of a Circle and it's proof: [http://youtu.be/xMXYJ9UeF4I](http://youtu.be/xMXYJ9UeF4I) .\r\n\r\n------------------------------------------------------\r\n\r\nSUBSCRIBE via EMAIL: https://mes.fm/subscribe\r\n\r\nDONATE! ʕ •ᴥ•ʔ https://mes.fm/donate\r\n\r\nLike, Subscribe, Favorite, and Comment Below! \r\n\r\nFollow us on:\r\n\r\nMES Truth: https://mes.fm/truth\r\nOfficial Website: https://MES.fm\r\nHive: https://peakd.com/@mes\r\n\r\nMORE Links: https://linktr.ee/matheasy\r\n\r\nEmail me: contact@mes.fm\r\n\r\nFree Calculators: https://mes.fm/calculators\r\n\r\nBMI Calculator: https://bmicalculator.mes.fm\r\nGrade Calculator: https://gradecalculator.mes.fm\r\nMortgage Calculator: https://mortgagecalculator.mes.fm\r\nPercentage Calculator: https://percentagecalculator.mes.fm\r\n\r\nFree Online Tools: https://mes.fm/tools\r\n\r\niPhone and Android Apps: https://mes.fm/mobile-apps","tags":["mathematics","calculus","science","stemgeeks","palnet","proofofbrain","education","stem","math"]}}}" | ||||||||||||
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I don’t always sketch polar coordinate curves but when I do I usually check for any symmetric properties to save time ;) View video notes on the Hive blockchain: https://peakd.com/@mes/video-notes-polar-coordinates-symmetry
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