Forgot something important. If the number in front of there is odd, the number of leaves is the same as that number. If even, number of petals is 2x that number.
this channel is so clutch. 2 weeks ago I was watching a video on rotational kinetic energy for physics and now I'm looking at polar coordinates for Specialist maths. Keep up the good work
Thank you soo much for being thorough in your explanation, and pointing out what part does what. You have no idea how much videos 14-18 have helped me understand the topic. no longer is it a grind on a calculator, inserting random values, until I get the desired result. Thanks to you I have a system with which to plot these roses in under a minute! Not all heroes wear capes Professor, and you are certainly one of those!
In principle, the even coefficient of Thetta means the number of small angles (or number of halves of a leaf) in the 1st 90 degrees; therefore, the No of complete leaves in the 1st 90 degrees is those given halves of a leaf divided by 2 (i.e. 6 halves of a leaf in 3 cos(6x) divided by 2 giving us 3 complete leaves) BECAUSE 1 leaf is made up of 2 small angles/2 halves of a leaf. For the whole circle/360 degrees, you then multiply the No of complete leaves in the 1st 90 degrees by 4. Generally, take the coefficient of Thetta times 2 to find the total No of leaves.
The best way to see that is to draw y = cos ( 2 theta) and y = cos (3 theta) and then using a highlighter, then highlight the part of the curve that corresponds to the angle range from theta = 0 to theta = 90 degrees.
Sir my english language is very weak. Can you tell me why you devide 2 all time from 360° with theta's coefficient in r = 3cos 2(theta)or some other sums you have done this videos. But in your other video you don't devide 2 when you drawn the graph of r=3cos(theta) or 3cos 5(theta). It would be better if you clear my doubts. Thank you!
For even angle cosine functions (cos 2 theta) or cos (4 theta) the number of leafs = 2 x the number of theta. This is found by plugging in number for theta and solving for r
This video shows the effect of changing the coefficient in front of the angle. What you are requesting can be found when viewing the other videos in the playlist.
+Michel van Biezen Example: ONLY the graph/the drawing of r=3cos6θ { 0 ≤ θ ≤ π/2 } is shown. The task is to find the equation of the graph, and the restrictions being used, given only its graph/drawing.
With the cosine function, we must divide by 2 in order to determine the number of "petals". Try it with the function: r = cos (theta). There will be 2 complete leaves when you graph that function.
Forgot something important. If the number in front of there is odd, the number of leaves is the same as that number. If even, number of petals is 2x that number.
That is a good observation !
Dude that's the next video in the series just sayin ya know
Thanks for bringing that up. I was stuck on a homework problem.
HELP BRO I LITERALLY ALREADY GRAPHED IT OMG
this channel is so clutch. 2 weeks ago I was watching a video on rotational kinetic energy for physics and now I'm looking at polar coordinates for Specialist maths. Keep up the good work
Glad you found us. Welcome to the channel!
Thank you soo much for being thorough in your explanation, and pointing out what part does what. You have no idea how much videos 14-18 have helped me understand the topic. no longer is it a grind on a calculator, inserting random values, until I get the desired result. Thanks to you I have a system with which to plot these roses in under a minute! Not all heroes wear capes Professor, and you are certainly one of those!
In principle, the even coefficient of Thetta means the number of small angles (or number of halves of a leaf) in the 1st 90 degrees; therefore, the No of complete leaves in the 1st 90 degrees is those given halves of a leaf divided by 2 (i.e. 6 halves of a leaf in 3 cos(6x) divided by 2 giving us 3 complete leaves) BECAUSE 1 leaf is made up of 2 small angles/2 halves of a leaf. For the whole circle/360 degrees, you then multiply the No of complete leaves in the 1st 90 degrees by 4. Generally, take the coefficient of Thetta times 2 to find the total No of leaves.
Sir... Can u please upload this types of tricks for cartesian curves also... Please sir... 🥺🥺
Its so much simpler than I thought. Thank you for breaking down the degree measurement.
Glad it was helpful! 🙂
Thanks so much! I like this method a lot better than the one my professor taught us
OMG, THANK YOU SO MUCH!!!
THIS HELPS ME WITH MY ASSIGNMENT!!!
you are a life saver
thank you so much sir
My favorite part was when you'd begin to form the petals and you could watch it all come together, knowing how it's done
It is quite interesting how it works.
You are a life saver thank you!
Loved it! Very clear and easy to understand. Thank you
Glad it was helpful! 🙂
You're a legend
I am from Bangladesh.very nice understanding systems.
Thank you. Welcome to the channel! 🙂
Me salvaste, gracias.
Thank you so much. ❤
Is it a must to plot a table?because you just told us the easiest way to plot this graph
It is not "required" but in some cases it is the easiest way.
Thank you so much your video really helped!!
You're welcome! 🙂
muito bom, me ajudou muito, parabéns!
Thank you so much…a very helpful video 👌🏻👏🏻👏🏻👏🏻
Glad it was helpful! 🙂
Good class❤️❤️❤️
if the number beside the theta determines how many leaves there are then why in "r=cos5(theta)" does that function only have 5 leaves? and not 10?
wait is it only even numbers that the leaves are doubled?
The best way to see that is to draw y = cos ( 2 theta) and y = cos (3 theta) and then using a highlighter, then highlight the part of the curve that corresponds to the angle range from theta = 0 to theta = 90 degrees.
@@MichelvanBiezen thank you!!!
Sir my english language is very weak. Can you tell me why you devide 2 all time from 360° with theta's coefficient in r = 3cos 2(theta)or some other sums you have done this videos. But in your other video you don't devide 2 when you drawn the graph of r=3cos(theta) or 3cos 5(theta). It would be better if you clear my doubts.
Thank you!
For even angle cosine functions (cos 2 theta) or cos (4 theta) the number of leafs = 2 x the number of theta. This is found by plugging in number for theta and solving for r
What if you are given the range of theta....say from 0 to 180°?
Then you stop drawing when you rach 180 degrees.
why pick four similar examples, instead of switching it to one with sine function and examples when the number in front of theta is odd
This video shows the effect of changing the coefficient in front of the angle. What you are requesting can be found when viewing the other videos in the playlist.
Thank you so much
You're most welcome
Who is the genius who doesn the thumbnail and how is it done, which program?
That genius is my wife who makes all of the thumb nails in paint.
@@MichelvanBiezen She deserves some type of award, they're very impressive 🙂
I think, as a chemistry student, that this is actually linked to orbitals, atomic orbitals theory... Just wondering...
It may look like it, but isn't. The Schrodinger equations dictate the shape of the orbitals. (See the quantum mechanics videos on this channel.)
Thank you, vdeo was very helpful.
It's very helpful to me
Excelente video, saludos desde venezuela
Welcome to the channel!
Given the graph of a polar rose that has been restricted , how do you determine its equation and the restrictions being used?
+Javi Lasala
Can you give us an example?
+Michel van Biezen Could I have your email? This is mine: josejavier66.lasala@gmail.com
+Michel van Biezen Example: ONLY the graph/the drawing of r=3cos6θ { 0 ≤ θ ≤ π/2 } is shown. The task is to find the equation of the graph, and the restrictions being used, given only its graph/drawing.
I wish he was my instructor.
Why are you multiplying the denominator by 2 everytime
With the cosine function, we must divide by 2 in order to determine the number of "petals". Try it with the function: r = cos (theta). There will be 2 complete leaves when you graph that function.
Big thanks
Big you're welcome!
How do you know how wide each leaf is?
We show how to do that in the calculus videos, when we show how to find the area of each leaf.
@@MichelvanBiezen Thanks
Thank you
You're welcome
Watched this twice
O god