polar

1. Need help with polar form

For example let's take - 1 + sqrt(3) i I want t change the above expression into polar form. I know how to change it to polar form in the form of r*cis(thetha) I know how to get r and thetha, but my issue lies with getting the exact thetha value (meaning I want the answer in a fraction...
2. Polar co-ordinate transformations: Proof of x(dx/dt) + y(dy/dt) = r(dr/dt)

Standard transformation from Euclidean to Polar co-ordinates: x = rcos(@) and y = rsin(@) with r = radial distance from origin and @ the angle. Various problems I've come across state: x^2 + y^2 = r^2 which solves easily if you remember cos^2@ + sin^@ = 1, and then go on to state, x(dx/dt) +...
3. triple integral in polar coordinate

why x is p(cosθ)(sinφ) ? and y=p(sinθ)(cosφ)? z=p(cosφ) As we can see, φ is not the angle between p and z .......
4. double integral in polar form

can someone explain about the formula of the circled part? Why dA will become r(dr)(dθ)?
5. polar graph

here's a list of polar gra[h that i dont understand... taking the first and second example , r = a cos theta , r = a sin theta why the center line of first graph is at x -axis ? why the second one is at y -axis ? and, where's the theta ? i didnt see it in figure
6. limit of polar integral

by using polar integral , find the area common to the circle r=3cos theta and the cardioid r= 1 + cos theta in the first quadrant I dont understand the solution provided by the author , why for region 2 , the limit of theta is from pi /3 to pi / 2 , can someone explain on it ?
7. Polar equation of a cycloid?

I understand a-f but I don't understand what my teacher is trying to imply on g. It looks like a cycloid in the middle there. Can anyone get me started?

10. Conversion: Polar form to rectangular form.

r=2cos(theta) r=2(x/r) r^2=2x x^2+y^2=2x x= rcos(theta) the answer in the book is (x-1)^2+y^2=1
11. Polar Coordinates r=1+2cos(thetta)

desmos.com/calculator So, reviewing Polar coordinates today, after learning it yesterday, I see that 0 degrees = 3, so then we plot it on 3 and it makes sense, however, take for example, 210, it is -.7, yet it is graphed on the 4th quadrant , instead of the third? Why is that? I cannot grasp...
12. Polar coordinates to Cartesian coordinates

Convert the system in the polar coordinates r'=(1-r), theta' =sin(theta/2)^2 into cartesian coordinates.
13. Polar Coordinate

I have a Praxis test coming up and need a bit of help with this question. Which of the following gives the rectangular coordinates of the point in the xy plane with polar coordinates (3, 4pi/3) I am looking more for a way to help solve this question and any tricks to help me remember. thanks
14. Tensor vector field ( Cartesian to polar coordinates) Help

Hi I have the following question with the answer but need to know to know the steps taken to derive the solution. Q) Consider the vector field , defined on a flat 2D space of Cartesian coordinates : V (u) = ( x +y ) ( x - y ) Find the V (a) after changing to polar coordinates...
15. Am I wrong for this polar conversion?

Prof just put exam solutions, and I think he is wrong. Basically the question asked to convert a double integral in terms of x and y and to a polar integral (just rewrite it... dont solve it). I had the limits correct, but for the actual function the solutions says it should be...
16. Domain of theta for a polar equation

Hello! I was wondering if there is a way to determine the domain of theta for a polar equation so that the graph creates 1 full rotation back to the origin and no more. For example, if I had the polar equation r=9sin2(theta), I can see that it takes from theta=0 to theta=pi for the graph to go...
17. Circle Polar Problem

\int_{0}^{\pi/2}\,\,\int_{16}^{4x}\,\, ?\,\, r \,\, dr \,\, d\theta - How can the integral be made polar? Part A: ? Part B \int_{0}^{\pi/2}\,\, d\theta = \theta evaluated at 0 lower bound and \pi/2 upper bound [\pi/2] - [0] = \pi/2
18. e polar problem

How were the r limits of integration found? Since it was a semi-circle, it was easy to see how the \theta limits of integration came about. \sqrt{4 - y^{2}} = 0 4 - y^{2} = 0 y = \pm 2
19. sine polar problem

\int_{?}^{?}\,\,\int_{?}^{?} \sin^{2}(r)(1)\,\, r \,\,dr \,\, d\theta Part A. \int_{?}^{?} \,\, \sin^{2}(r)\,\, r\,\, dr u = r du = 1\,\, dr (r)(du) = (r)\,\, dr = r \dfrac{-\cos^{3}(r)}{3} evaluated at ? and ? Part B. \int_{?}^{?} \,\, 1 \,\, d\theta = \theta evaluated at ? and ...
20. Polar Coordinate Double Integration

Evaluate the given integral by changing it to polar coordinates \int\,\,\int_{D}\,\, e^{-z^{2}-y^{2}}\,\, DA where D is bounded by the semicircle x = \sqrt{4-y^{2}} and the y axis (x = 0) \int\,\,\int_{D}\,\, e^{-z^{2}-y^{2}}\,\, DA = \int_{-(\pi/2)}^{\pi/2}...