Questions on polar coordinates, a coordinate system where points are represented by their distance from the origin ($r$) and the angle the line joining the point and the origin makes with the positive horizontal axis ($\theta$).

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2answers
23 views

Eliminate the parameter

Given the parametric equations: $x = sin(\frac{1}{2} \theta)$ $y = cos(\frac{1}{2} \theta)$ Eliminate the parameter. I am completely lost. Please help.
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3answers
37 views

Find polar coordinates $(r, \theta)$ of the point, where $r > 0$ and $0 \leq \theta < 2\pi$

Given these Cartesian coordinates: $(2,-3)$ This is my fourth problem of this type, I solved the other 3, but this one has weird numbers and I don't know what to do. $\tan\theta = -\frac{3}{2}$ ...
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0answers
22 views

line integral problem, stuck in the curve

Problem: A force field is given in polar coordinates by the equation $$F(r,\theta)= (-4\sin (\theta), 4\sin (\theta)).$$ Compute the work done in moving a particle from the point $(1,0)$ to the ...
3
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2answers
39 views

Is it possible to convert the polar equation $\ r = k \cos (\theta n) + 2$ into cartesian form?

Is it possible to convert the polaer equation $$\ r = k \cos (\theta n) + 2$$ into cartesian form? Here, $k$ is some constant and $n$ is any positive whole number greater than $2$. The ...
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2answers
36 views

Changing the order of integration on a rectangular and polar region

change the order of integration for the following integral from dydx to dxdy, and from dydx to polar coordinates. $$ \int \int f(x,y) dydx$$ where $$ 0≤y≤(-x^2)+2 $$ $$ 0≤x≤1$$ From dydx to dxdy $...
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0answers
27 views

Eliminate the parameter to find a cartesian equation for the curves

For the first part I am just unsure as to how the book has a different answer than mine. The book has the answer $y = \frac{3}{4} x - \frac{1}{4}$ but given the functions $x(t) = 3 - 4t$ and $y(t) = ...
4
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4answers
66 views

How do I find the Integral of $\sqrt{r^2-x^2}$?

How can I find the integral of the following function using polar coordinates ? $$f(x)=\sqrt{r^2-x^2}$$ Thanks!
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1answer
81 views

Solve differential equation by using polar coordinates

For $\alpha, \beta>0$ the differential equation, I am trying to solve, is given by $$\begin{pmatrix}\dot x_1\\\dot x_2\end{pmatrix}=\alpha\sin(x_1^2+x_2^2)\begin{pmatrix}x_2\\-x_1\end{pmatrix}+\...
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0answers
15 views

Polar Coordinates Volume of Solid, Angle for integration?

I'm trying to understand how to find the angle for the integration in polar coordinate form for a solid. Here's an example of what I'm trying to solve: Find the volume of the solid bounded by the ...
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1answer
39 views

Cauchy rieman equation. What is u?

Using cauchy rieman equation, i want to show the function is analytic. So i want to decompose from f(z) to two term (real part and imaginary part) With rectangular form or polar form. But it is so ...
1
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0answers
21 views

Cartesian and Polar Coordinates, proving the same number-pair

The question states: Prove that a necessary and sufficient condition for a point to be represented by the same number-pair (a,b) both cartesian and polar coordinates is that it lies on the initial ...
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3answers
447 views

Why are there two versions of a polar equation for a circle from geometric form

In class today we learned that a rectangular/geometric equation for a circle such as $x^2+(y-5)^2 = 9$ can be converted into a polar equation by reducing it to the quadratic equation $r^2-10r\sin \...
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0answers
21 views

Calculating a likely position in 0.5 seconds with only the knowledge of the last second (x,y coordinates)

I have x,y coordinates for football players (22) at a rate of 10 records per second - for an entire football match. I have created an animation of the match with the player locations updates at a ...
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0answers
73 views

Solve a Laplace in Poolar Coordinate under two minutes?

I trouble with calculating the following example from previous exam with short solution on this Link. OP says there is a Laplace ٍPoolar Coordinate: $\frac{1}{r}\frac{\partial}{\partial r}(r\frac{\...
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2answers
80 views

Solve $z^5=-32$ and draw its solutions in complex space, then describe their characteristic geometrical property.

I'm solving past exam questions in preparation for an Applied Mathematics course. I came to the following exercise, which poses some difficulty. If it's any indication of difficulty, the exercise is ...
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2answers
40 views

Can we convert polar to rectangular when we are given $(1,\theta )$ where $ r=1$ and $0\le \theta <2\pi $?

Can we convert polar to rectangular when we are given $(1,\theta )$ where $ r=1$ and $0\le \theta <2\pi $?
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1answer
49 views

How to think in terms of Polar Coordinates?

I am currently studying Polar Coordinates and many times I've noticed that one converts polar equations in cartesian form to do further analysis. Is there a way to think in terms of Polar Coordinates? ...
0
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1answer
14 views

Polar angle of a given point

How to find out polar angle of a given point $A(x_1,y_1)$ relative to another point $B(x_2,y_2)$ in a 2D space?
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0answers
45 views

Convert Polar Equation to Rectangular Equation

I have been trying to convert the polar equation to rectangular. $U(1,\theta) = 10+3*sin(\theta)-10*cos(2*\theta)$ I started off my multiplying everything by r and using the trig identity for cos($...
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0answers
35 views

How can I know when I can and can't integrate from $0$ to $2\pi$?

I'm taking vector calc right now (maybe the same as Calc 3?) and I think I'm forgetting something I used to understand. I know sometimes when you are integrating in polar coordinates (and probably ...
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2answers
31 views

Intersection between roses with given polar equations

$ r_1 \ = \ 4 \sin(3 \theta) \ $ and $ \ r_2 \ = \ 3 \cos(3\theta) \ $ a) find the solutions to the system using polar coordinates I was able to solve this by setting $ \ r_1 \ $ and $ \ r_2 \ $ ...
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2answers
27 views

Converting polar equation to cartesian coordinates

I have been trying everything to convert the polar equation $r=\frac{2}{1-\cos(\theta)}$ to cartesian coordinates but I simply didn't manage to know the right answer. Please help me..
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0answers
31 views

Evaluating an integral in polar coordinates with exponential and sec^2

I'm stuck trying to find the closed form expression of an integral. I was able to upper bound it, but if anybody can help me find a way to determine the exact answer, it would be appreciated. Thanks ...
0
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1answer
31 views

How to multiply a number in polar form by $-1$

Given a number in the form of $a\angle b$, what happens if I multiply it by $-1$? Is it $-a\angle -b$ or $a\angle −b$? Does a negative modulus even make sense? Thanks!
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2answers
43 views

$r=a\sin \theta$ $r=a\cos \theta$ intersect at right angles

In Stewart's Calculus book, he asks: Show that the curves $r=a\sin \theta$, $r=a\cos \theta$ at right angles. I do not understand the question. It is clear that they meet for example when $\...
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1answer
13 views

Trig Identities when converting to polar form

Been practicing conversions from rectangular form to polar form but got stuck on one question. rectangular form: $\frac{1}{1+j\omega}$ polar form: $r = \left|\frac{1}{1+j\omega}\right|$, $\phi = -\...
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1answer
24 views

Converting coordinates

I am having huge trouble converting between cartesian to polar and to spherical. I need these methods for my limits of integration in most cases but using the formulas never seem to work, I just ...
1
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2answers
31 views

parametric polar equation of a circle

I discovered that Mac's Grapher has a parametric polar mode, i.e. where $r$ and $\theta$ can be specified in terms of a parameter, usually $t$. I am attempting to convert the generic equation for a ...
5
votes
2answers
122 views

How can $e^a = 0$ when integrating?

I was doing a question which asked me to turn the following into polar equation:$$(y + x − x(x^2 + y^2))\frac{dy}{dx} = y − x − y(x^2 + y^2)$$ With a lot of messy algebra I can get it down to: $$\...
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5answers
53 views

Finding a Coordinate on a circle using radius, angle, and origin

I am trying to calculate a point on a circle using an angle and a different point. With this picture, I know the origin O, the radius r, the angle A, and the point B. Now I want to find the point C....
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0answers
12 views

Geometric or arithmetic sequences in polar coordinates

While studying the properties of the logarithmic spiral, I came across a theorem stating that secant lines drawn from the origin (pole) to the spiral form a geometric progression. I was interested to ...
1
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1answer
26 views

Polar equations (further question)

Consider the polar equations of the form $r=a\cos(b\theta)$ and $r=a\sin(b\theta)$. What is the nature of the graphs of these two polar equations and then summarize some generalizations with respect ...
1
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2answers
61 views

Why does $\sin\phi=r\frac{d\theta}{ds}$ and $\cos\phi=\frac{dr}{ds}?$

The relation between $p$ and $r$ where $p$ is the length of the perpendicular from the fixed point $O$ on the tangent to the curve at any point $P$ is called pedal equation of the curve. I want to ...
1
vote
1answer
33 views

Integrating using polar co-ordinates

Hey I've just finished an exam paper and just am stuck with one question. It's something that usually makes sense to me but for some reason I can't get this one: Let $R = \{(x,y) : x,y ≥ 0, x^2 + ...
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0answers
23 views

Converting a vector $v \in \mathbb{R}^2$ given in Polar coordinates to Cartesian coordinates

I know that switching inbetween Polar coordinates and Cartesian coordinates in $\mathbb{R}^2$ can, on suitable open subsets of $\mathbb{R}^2$, be done via $(x, y) = (r cos \theta, r sin \theta)$. Let $...
2
votes
3answers
39 views

Integral conversion to polar coordinates - bounds

I have an integral $$\int_0^1 \int_0^1\sqrt{x^2+y^2}\ dxdy $$ and its result is $\approx0.765...$ I convert it to polar coordinates and get $$\int_a^b \int_c^dr\ drd\phi $$ But how can i compute $...
0
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1answer
22 views

Calculating the area between a petal and a circle (Polar Coords)

The question states: The graph of $2\cos(3\theta)$ has three petals (also called "leaves" or "lobes"). The intersection of one of those petals with the circle $r = 1$ is shaded in the figure. Find ...
2
votes
2answers
62 views

Sketch the heart and indicate its orientation with arrows $ r = 1 - \cos(\theta)$. Find the area enclosed by the heart

Hi all I am trying to figure out how to sketch the heart. Here is what I have tried so far: $$r = 1 - \cos(\theta) \\ r(r = 1 - \cos(\theta)) \\ r^2 = r - r\cos(\theta) \\ $$ Use the fact that $$r =\...
0
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1answer
54 views

The Laplacian in Polar Coordinates

When solving the Laplacian in polar coordinates, $x=r\cos\theta$ and $r^2=x^2+y^2$. When finding $\frac{\partial u}{\partial x}=\frac{\partial u}{\partial r}\frac{\partial r}{\partial x}+\frac{\...
0
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1answer
26 views

Raising Polar to the Power

Ok guys, I'm back! This is gonna be my last question here, as I have practically finished test review. Raise to the the power: b ) $(8 cis(120 ^\circ)))^{1/3}$ ... Well for this there are two ...
4
votes
4answers
105 views

Find the two square roots of $i$

I have this question I am stumped upon for my Test-Review: Write $i$ as a complex number in polar form. Use the result and DeMoivre's Theorem to find the square roots of $i$. I got the first ...
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3answers
54 views

Converting into rectangular form

I have 2 related questions: First: Let $z_1 = 2+2i$ and $z_2 = 2-2i$. Find $z_1z_2 $ in rectangular form. I have no idea... I'm also clueless about this question: Change the following to ...
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1answer
43 views

Find the area bounded by $r=6\sin(2\theta)$

Winplot plot: I tried this: $$A = 4 \cdot \frac 1 2 \int_0^{\pi/2} (6\sin(2\theta))^2 d\theta$$ Is that right? How about $$A = 8 \cdot \frac 1 2 \int_0^{\pi/4} (6\sin(2\theta))^2 d\theta$$
0
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1answer
26 views

Find the area inside $r=2+2\sin(\theta)$ but outside $r=4\sin(\theta)$.

Winplot plot: I tried this: $$A = 2 \frac 1 2 \int_0^{\pi/2} (2+2\sin(\theta))^2 - (4\sin(\theta))^2 d\theta + 2 \frac 1 2 \int_{\pi}^{3\pi/2} (2+2\sin(\theta))^2 d\theta$$ Is that right? How ...
0
votes
0answers
34 views

Find the volume(solid) , transform rectangular function to polar function

if want find volume of this problem Under $ f(x)=x^2+y^2-4 $ and inside $ x^2 + y^2=9$ in plane $z=0$ Can I use this integration in polar functions? $$\int_0^{2\pi} \int_2^{3} (r^2 - 4) r dr\,d\...
0
votes
1answer
46 views

Converting to polar coordinates in integral over $\mathbb{R}^{n}$

I have an integral equation $$\int_{\mathbb{R}^{n}}F(x)dx=1$$ for $F(x):=\frac{C}{(1+|x|^{2})^{\frac{n+1}{2}}}$. And I want to convert the above integral equality to polar coordinates. Am I right in ...
0
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1answer
29 views

Converting Polar Coordinates to Regular Coordinates

If you guys didn't know, I have my quiz tomorrow and I have one last thing to ask to this Community! I am completely confused on how to convert polar coordinates to regular coordinates. The teacher ...
0
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5answers
27 views

Labeling Negative Polar Coordinates

i have a quiz coming up tomorow and i have this major question.. its a question about how to plot it exactly when it is negative. Let me go through the whole set: 1) ($4$ , $60^\circ$) 2)($-4$ , $...
0
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1answer
31 views

Triple Integration of gravitational potential

Integrate $\int_{0}^{2\pi } \int_{0}^{a} \int_{0}^{\pi/2} \frac{ G\rho r^2 sin \theta}{ {(r^2-2rt cos \theta + t^2 )}^{\frac{1}{2}}} d \theta dr d \phi$, where $\rho, t $ are constants. Sorry for ...
0
votes
1answer
34 views

Changing a rectangular equation into polar equation

Find the polar equation that has the same graph as the given rectangular equation. I have used the method of substituting $r \sin θ$ for $y$ and $r\cos θ$ for $x$. $x^2=8(2−y)$ $r^2\cos^2(θ)=8(2−r\...