Rectangular Equation to Polar Equations, Precalculus, Examples and Practice Problems
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- čas přidán 16. 05. 2017
- This precalculus video tutorial explains how to convert rectangular equations to polar equations. This video contains plenty of examples and practice problems. It provides all of the formulas that you need to convert a rectangular cartesian equation into polar form using trigonometric functions such as sin, cos, tan, sec, csc, and cot.
Solving Trig Equations - Finding All Solutions:
• Solving Trigonometric ...
Solving Trig Equations With Multiple Angles:
• How To Solve Trigonome...
Solving Trig Equations With Double Angles:
• Solving Trigonometric ...
Law of Sines:
• Law of Sines - Basic I...
More Examples - Law of Sines:
• Law of Sines, Basic In...
Area of an Oblique Triangle:
• Area of an Oblique Tri...
______________________________
The Height of a Triangle - Heron's Formula:
• How To Calculate The H...
Law of Cosines:
• Law of Cosines, Findin...
Polar Coordinates:
• Polar Coordinates Basi...
Polar Equations to Rectangular Equations:
• Polar Equations to Rec...
How To Graph Polar Equations:
• How To Graph Polar Equ...
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Complex Numbers - De Moivre's Theorem:
• Complex Numbers In Pol...
Dot Product of Two Vectors:
• Dot Product of Two Vec...
Trigonometry Final Exam Review:
• Trigonometry Final Exa...
Final Exams and Video Playlists:
www.video-tutor.net/
Full-Length Videos and Worksheets:
/ collections
Graphing Polar Equations: czcams.com/video/IL2mM4CppGg/video.html
De Moivre's Theorem: czcams.com/video/f0uOujml3QU/video.html
The Dot Product - Vectors: czcams.com/video/Ytn070pkn54/video.html
Next Video: czcams.com/video/jO4lwddfeDA/video.html
Tangent Line Equations - Calc 2: czcams.com/video/ImtzLh8KhIE/video.html
5.6 million subscribers from a bunch of math, science and physics tutorials made by a single person. That is an amazing achievement.
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@@nomadicstrength 7.87 now :)
7.96, almost 8 mill!!!
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My teacher really told us to learn this by ourselves wow.
MY teacher didn't even told us. he just assumed we knew it
Wait...you guys have a teacher?
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Who else just likes the voices of the people teaching
I personally don’t
Man, I was watching the examples hoping one was similar to my homework problem, and BAM y^2=4x pops up and you made me understand something so simple. thanks!
Thank you so much! I never understood this, and here I am an hour before my Precalculus final learning it and I finally understood it. Thank you!!
Thank you so much!! The practice problems really helped to consolidate the formulas!
This guy taught the topic better than my college professor. THANK YOU!
Professor Organic Chemistry Tutor, thank you for another fantastic video/lecture on How to convert Rectangular Equations to Polar Equations in Calculus. This material will also be used in Calculus Three and other technical courses in Science and Applied Engineering. This is an error free video/lecture on CZcams TV with the Organic Chemistry Tutor.
Thank you! This helped immensely!
Thank you for all your hard work. I have been teaching myself with these videos because I got COVID and don't want to fall too far behind in pre-calc.
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GRACIAS, llevaba una hora descifrando como hacerlo pero me acabas de salvar
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Thanks for the video!
But what if the equation has coefficients for x and y? Like
3x^2 + 2y^2 = 8
for the last one we should write Ω=π/3 + kπ because arctan(tan(x))=x if and only if x in -90 ° and 90°
thank you so much ❤❤❤
Thanks a lot
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Thank u so so much
I watched this video several times and practiced a few other problems, yet I got my final and went blank!!! So mad at myself right now. :( It's so easy yet WHAT THE HECK?!!!
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Thank you so much. What about this problem y^2=3x+3? Please I need your help on that.
omg thank u so muchhh
Thank you
I have got a question, with the rules given at 1:45, couldn't you always just sub in Rcosθ for x and Rsinθ for y? Why ever use any other method, is it because it is easier to simplify?
Thanks
at 6:38 , (x-3)^2 + y^2 = 9 is a circle, but r = 6cosx is a wavelike graph. Why the inconsistency?
*CALCULUS iii PLEASE*
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Something is amiss. I was looking for how to rewrite (5, -5) to Polar, but noting in the video helped.
The polar coordinate formula is (r,degree). Since the equation is x^2+y^2=r^2, you do 5^2+(-5)^2 which is 50 = r^2, so r= square root of 50. Then you do tan-1 to find the degree.
This says precalc but this has just been tossed on me during calc 3, never seen a polar equation outside of the polar rose before
How do you convert y=x to its polar form?
Y = X
Since Y = r sin θ and
X = r cos θ
Y/X = 1
r sin θ/r cos θ = 1
but. sin θ/ cos θ = tan θ
therefore,
tan θ = 1
θ = 45°
I hope I am correct.
7:33 There is actually only one answer here, not two. 'r' cannot equal 0 in this context. Since r is never equal to zero (it can be negative, though), you can divide both sides of the equation by r. This means that the second result, r=6costheta, is the only possible polar form. r=0 is the polar equation of a circle entered at the origin with no radius. This doesn't match up with the rectangular form of the equation, which indicates a circle centered at (3,0) with a radius of 3. Likewise with 9:24, 10:46. It's not that textbooks are omitting an answer; r=0 is not a valid answer at all in this particular context, despite the fact that it is a solution to the equation.
tysm, i was looking all over for this info
Actually, "r" can be equal to 0. To understand the reason that this solution isn't in textbooks, you need to think about what r=0 really means. It's just the point where the x and y axes cross. This point is already included in the second equation for "r," so saying that r=0 is simply redundant.
@@noahali-origamiandmore2050 You and I are in agreement.
@@noahali-origamiandmore2050 You and I are in agreement. I never claimed that r=0 is not a solution to the equation. But r=0 will not be helpful for writing the polar equation in rectangular form. I apologize if I didn't make this clear.
@@gentlemandude1 I actually never thought of using r=0 to convert back to rectangular form. Thx for the info.
5:27 wouldnt the answer be R = + or - 4
yes, but they return the exact same graph, a circle with radius 4, so it would be redundant
How to do
theta = pi/2
How the hell , at 4:40, when you divide R[blahblahblah] does the R not get affected? Surely it would be R divided by [blah blah] = 8 divided by [blah blah] instead you just go R = 8 divided by [blah blah]
it cancels out
I love you Sir. I owe you my college fees.
R = +4 or -4
y2=4x in this equation can I write only one answer... if i don't write R=0,
16:15
What!? Still searching CZcams for math help? Are the videos from 2006 really helping??
If it's the Organic Chemistry Tutor, Absofuckinglutely!!!!!!!!!!!!
What about xy=(Any number)
socratic.org/questions/how-do-you-convert-xy-1-into-polar-form
Bruh I’m still confused
Okay but you did not tell us why y=x(sqrt3) is not equal to 2pi/3 as well as pi/3
He neglects to explain this well. Essentially, our polar equation is just an angle, which means that any r-values, both positive and negative will satisfy the equation so long as they result in points that are on the ray defined by the angle pi/3, just as any x-values that lie on the line y=x*sqrt(3) will satisfy that equation. Since polar equations are not unique, 4pi/3 is also a valid answer. However, 2pi/3 is not a valid answer because that angle is not in the domain of the arctan function, and also points on that polar angle do not correspond to those on the line y=x*sqrt(3). I hope that this explanation helps, even if it is two years too late.
As for his pronunciation: give the guy a break, he puts a lot to time and effort into creating these videos for FREE. Consider showing a little gratitude.
@@gentlemandude1 Thank you and yes you are right. My pet peeves should be kept to myself. I will correct that
tired of this long ad. see ya
This helped so much. Thank you!!