︎►►📝Download my free blank polar coordinate systems to help you practice graphing: www.jkmathematics.com/blank-polar-coordinates-worksheet Also, MINOR CORRECTION: At 16:17 when I give the subtraction identity for cosine, I made a slight error. It should be cosAcosB + sinAsinB. I wrote a minus sign in between the terms by accident and did not catch it in the editing process since the final answer was not effected by the mistake (adding/subtracting 0 produces the same result!). I got lucky, but that will not always be the case when checking symmetry! Be sure to remember that it is (+) not (-). My apologies on that mistake!
Great video, polar was included in the new AP Precalculus and I needed a good refresh to be ready to teach students when I haven't done anything with polar in decades and your videos were clear and helpful. And y If you ever get to a precalculus series I will include you on my recommended resource list for students.
Very good, I am impressed. I admire your work, keep goint bro. You really making a good stuff. Thanks to people like, it is easier for us to understand very hard concepts)
Thank you for this video this helped me so much I was so confused on how to graph the thing and my previous difficulties with the unit circle only made it worse. Thank you so much for the good info and easily understandable content.
You're welcome! Glad the videos are helpful for you :) In the future if you take Calc 1 after precalc, be sure to check out my Calc 1 playlist as well!
How do you know to where do the cardioid/limacons’ points extend for the other angles? Like how do I know if it crosses or not trogh pi/4 for example, after sketching the graph with the quick method?
For the quick method, we really only look at where the graph would cross the vertical and polar axis. If you start looking at other angles, then it really isn't so "quick" anymore. You would be better off using the plotting points and symmetry method if you want to be that accurate. That being said, typically, you want to know the general shape of the different polar graphs, and that should help you draw them quickly in conjunction with the points on the polar and vertical axis for the quick method. If you really wanted to, you could plug in the angle, such as π/4, into the polar equation you are working with, and see what value of r is outputted, and then use that to help you determine where the graph crosses that angle in the coordinate system. But once again, at that point you might as well just plot points and use symmetry. The way I see it, the quick method is really just for sketching the curves super fast, which helps later on in Calc 2 such as when you need to draw a picture to help you figure out how to set up integrals to calculate area between polar curves. If you need to be more accurate with the graph, you want to plot points and use symmetry instead. Hope this helps!
For the plotting points and using symmetry method, you can pick whatever angles of theta you want to create some points. It is totally up to you. Now, you probably want to pick angles that are nice to evaluate for the given equation, so I recommend sticking with the most common angles of 0, π/3, π/4, π/6, π/2, π, 2π, etc. Those are usually the easiest to work with. Sometimes you can pick a weird angle like π/8 if that makes it easier to plug in, such as for the function r=cos(2θ). Because θ is multiplied by 2, using π/8 becomes convenient since 2 times π/8 is π/4, which is a nice angle to evaluate cosine at. Does that make sense? In general, just pick the most convenient angles. Hope this helps!
︎►►📝Download my free blank polar coordinate systems to help you practice graphing:
www.jkmathematics.com/blank-polar-coordinates-worksheet
Also, MINOR CORRECTION: At 16:17 when I give the subtraction identity for cosine, I made a slight error. It should be cosAcosB + sinAsinB. I wrote a minus sign in between the terms by accident and did not catch it in the editing process since the final answer was not effected by the mistake (adding/subtracting 0 produces the same result!). I got lucky, but that will not always be the case when checking symmetry! Be sure to remember that it is (+) not (-). My apologies on that mistake!
thankyouuu, u're a life saver
How do you only have 3.5k subscribers, you are incredibly underrated.
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Most underrated youtube channel, tysm for this video
Highly underrated video .shame on CZcams
I have to share this video to my lecture, maybe then he'll know how to tech his students a new topic correctly
OMG amazing explanation I love it, love it by the way biscuit is ingenious 😄
Thank you! Glad to hear the video was helpful :)
Great video, polar was included in the new AP Precalculus and I needed a good refresh to be ready to teach students when I haven't done anything with polar in decades and your videos were clear and helpful. And y If you ever get to a precalculus series I will include you on my recommended resource list for students.
Awesome! Thanks for sharing, glad the videos were able to help. Precalculus is definitely in my roadmap for future series to make one day!
Your style of teaching is too good.
Thank you! I appreciate the kind feedback :)
Really this is a very underrated channel. Very informative video indeed
Thank you so much. Great video
Thank you! 😊
Great video. It is a shame that it is so underrated.
Thank you so much for this explanation, I can't tell you how much help this was!
You're very welcome!
Thank you so much
Very good, I am impressed. I admire your work, keep goint bro. You really making a good stuff. Thanks to people like, it is easier for us to understand very hard concepts)
Thank you, I appreciate the kind feedback :) Feel free to share these videos with others!
Yor lessons are very helpful sir.thank you very much i really i appreciate your videos❤️🙏
Thank you for this video this helped me so much I was so confused on how to graph the thing and my previous difficulties with the unit circle only made it worse. Thank you so much for the good info and easily understandable content.
You're very welcome! Glad the video was able to help :)
Thank you very much you are saving my precalc grade in this new trimester bro. You are an awesome teacher🙏👍😎
You're welcome! Glad the videos are helpful for you :) In the future if you take Calc 1 after precalc, be sure to check out my Calc 1 playlist as well!
Thanks for the refresher on precalc lol. Even did r value analysis. you are the best
You're welcome! Glad to help :)
This video helped me a lot. You have earned my like and subscription :)
Thank you! Glad the video could help you!
Thanks!
You're welcome! And thank you for your generosity!
THANK YOU. SM.
How do you know to where do the cardioid/limacons’ points extend for the other angles? Like how do I know if it crosses or not trogh pi/4 for example, after sketching the graph with the quick method?
For the quick method, we really only look at where the graph would cross the vertical and polar axis. If you start looking at other angles, then it really isn't so "quick" anymore. You would be better off using the plotting points and symmetry method if you want to be that accurate. That being said, typically, you want to know the general shape of the different polar graphs, and that should help you draw them quickly in conjunction with the points on the polar and vertical axis for the quick method. If you really wanted to, you could plug in the angle, such as π/4, into the polar equation you are working with, and see what value of r is outputted, and then use that to help you determine where the graph crosses that angle in the coordinate system. But once again, at that point you might as well just plot points and use symmetry. The way I see it, the quick method is really just for sketching the curves super fast, which helps later on in Calc 2 such as when you need to draw a picture to help you figure out how to set up integrals to calculate area between polar curves. If you need to be more accurate with the graph, you want to plot points and use symmetry instead. Hope this helps!
Godd shit bro this shit saved me
I’m dumbest in math but you made it so easy Thankyou so much 😭❤️
You're welcome! Glad to help :)
Thanks for such a good video. Just to point out a mistake, at 16:18 the compound angle formula is wrong.
You’re welcome! And yes, I mention the small mistake in my pinned comment on this video. I explain what correction should be made there.
How do we know what thetha we will plug in the equation?
For the plotting points and using symmetry method, you can pick whatever angles of theta you want to create some points. It is totally up to you. Now, you probably want to pick angles that are nice to evaluate for the given equation, so I recommend sticking with the most common angles of 0, π/3, π/4, π/6, π/2, π, 2π, etc. Those are usually the easiest to work with. Sometimes you can pick a weird angle like π/8 if that makes it easier to plug in, such as for the function r=cos(2θ). Because θ is multiplied by 2, using π/8 becomes convenient since 2 times π/8 is π/4, which is a nice angle to evaluate cosine at. Does that make sense? In general, just pick the most convenient angles. Hope this helps!