Tagged Questions
1
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2answers
46 views
$f(x,y)=\langle y- \cos y, x \sin y\rangle$
$f(x,y)=\langle y-\cos y,x\sin y\rangle$
$C$ is the circle $(x-3)^2 + (y+4)^2 = 4$ orientated clockwise.
Relevant theorems:
Green's theorem (this is under the Green's theorem section of our book).
...
1
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1answer
51 views
How did theta become equal to 3pi/4 here?
How did theta become equal to 3π/4 in this particular example?
Find a set of polar coordinates (r,θ) of the cartesian point (-4,4)
such that -2π ≤ θ ≤ 2π and
a. r > 0 and θ > 0 b. ...
1
vote
1answer
61 views
Finding area between two polar curves using double integrals
I have a homework question that is asking me to find the area that lies:
Inside the curve $r=2+cos(2\theta)$
But outside the curve $r=2+sin(\theta)$
I think I'm supposed to be using a double ...
2
votes
2answers
93 views
Find Cartesian equation of $r=\theta$
I solved this problem, but I'm not sure my answer is correct as it seems very complex (compared to the polar equation). Did I make some mistake along the way or is it the right solution?
$$r=\theta$$
...
2
votes
1answer
87 views
Find a Cartesian equation of $r = 4\cos\theta$
I was able to figure the substitutions inside the equation, but I'm stuck with the equation's manipulation that will give me the solution. What would be my next step?
$$r = 4\cos\theta$$
$$r^2 = ...
4
votes
0answers
73 views
Parametrization of a curve in polar coordinates
I'm trying to change this parametrics equations to polar coordinates
$$ X(t) = 2\cos(t) - \sin(2t) \\
Y(t) = 2\sin(t) - \cos(2t) $$
What i tryed to do was raise the two equations squared, sum ...
3
votes
1answer
44 views
polar coordinates ..question about the answer from the solution manual
Im trying to figure out but for some reason I dont know how to...could someone please tell me how did they get this answer from the solution manual....they skipped steps so I have no idea
0
votes
1answer
594 views
Find the area of the Rose's petal.
If a Rose leaf is described by the equation $r = \sin 3\theta$, find the area of one petal.
0
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3answers
92 views
Cartesian and Polar Coordinate
I should give the Cartesian Coordinates $(x,y)\in \mathbb{R\times R}$ and Polar Coordinates $(r,\varphi)\in R^+\times [0,2\pi)$ of the following Complex Numbers:
a) $z_{1}=-i$
b) $z_{2}=\sqrt{3}+i$
...
1
vote
2answers
46 views
Polar coordinates - issue with direction denoted by angle
Convert $1-\sqrt{3}i$ to polar coordinates $(r,\varphi)$.
I started by computing $r=|1-\sqrt{3}i|=\sqrt{1^2+\sqrt{3}^2}=\sqrt{4}=2$. When I tried to compute the angle I did something like
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1
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1answer
506 views
Cardioid given by the polar equation $r = 1 − \cos(\theta)$
Let $C$ be the cardioid given by the polar equation $r = 1 − \cos(\theta)$ , $−\pi \le \theta \le \pi$.
(a) Find the intersection points of the curve with the line $\theta = \pi/4$.
(b) Find the ...
1
vote
0answers
145 views
(Calculus 3) Having trouble finding the polar equation of a hyperbola.
Eccentricity e=sqrt(2), and one vertex is located at (2,0).
I do know that if the vertex is located at (2,0), then the directrix is 2 units from the vertex. I am not sure how to find the location of ...
0
votes
1answer
257 views
Magnitude of average velocity..
A particle is at the position with Cartesian components $(5.0 m, 4.0 m)$ and $5.0 s$ later it is at the position with components $(8.0 m, 0.0 m)$. What is the magnitude of its average velocity?
I ...
1
vote
1answer
93 views
The point C has coordinates (2,k) and the distance from A to C is 5. Find the 2 possible values of the constant k
The coordinates of A are (6, -2)
I have managed to do every other question in this section but this one, my brother tried to help but just drew a graph and the answers without explaining it, i dont ...
1
vote
4answers
164 views
Find the length of a curve
Find the length of the following curve:
$r(t) = e^{-t} \sin(t)+e^{-t}\sin(t) i$ for $0 \leq t\leq 1$.
Any ideas?
1
vote
1answer
1k views
Find the equation in polar coordinate form for a straight line through the points with polar coordinates (4,0) and (4,π/3).
Find the equation in polar coordinate form for a straight line through the points with polar coordinates $(4,0)$ and $(4,π/3)$.
Here's my steps:
1.Write the two points in cartesian coordinates: the ...
1
vote
1answer
80 views
Maximum point of a polar function
I have a curve C with polar equation
$$r^2 = a^2\cos{2\theta} $$
And I am looking to find the length $x$ when $r=max$
Judging from the equation:
$$r = \sqrt{a^2\cos{2\theta}} $$
R will be maximum ...
1
vote
1answer
197 views
Find the area of the region determined by two curves
Find the area of the region $R$ given by two curves.
So the region $R$ describes the area that is common between the two curves:
$$\begin{align*}
\text{Function 1: } r&= 2\sin(\theta)\\
...
5
votes
2answers
756 views
Is $r=2\cos(\theta)$ a one-petal polar function?
I'm currently learning about polar functions and their graphs in precalculus, and one of the questions on my homework is to identify the shape of the function $r=2\cos(\theta)$. We were taught that ...
1
vote
1answer
354 views
Replace the Cartesian equation $(x-5)^2 + y^2 = 25$ by an equivalent polar equation.
Replace the Cartesian equation $(x-5)^2 + y^2 = 25$ by an equivalent polar equation.
Let $t= \theta$, $r=5$, $x=r\cos t$, $y=r\sin t$.
I began with $x=5\cos t-5=5(\cos t-1)$ and $y=5\sin t$. Is that ...
0
votes
2answers
92 views
Laplacian in polar coordinates
I am stuck with an exercise that requires me to find the Laplacian $\Delta u=(D_x^2u+D_y^2u)$ of a 2d-function $u$ in polar coordinates (in the standard Euclidean plane).
I found the following ...
0
votes
1answer
214 views
Transform integral into polar coordinates
At university we are given a voluntary hand in in the use of maple/matlab, in that
regard I have a double integral I am in dire need to compute, using first cartesian then polarcoordinates.
...
1
vote
2answers
95 views
Polar Coordinates
It's been ages since i did any coordinate conversions, and typically i have these two which i just can't manage to solve by myself.
I want to express the circle $x^{2}+y^{2}<4, x<0 $
The Area: ...
1
vote
1answer
187 views
Help needed with partial derivatives and polar coordinates, missing term.
I have a missing $\frac{1}{r}\partial_r$ -term (notice the question mark) but cannot see why, could someone hint where I am doing mistake.
2
votes
1answer
168 views
Explain Dot product with Partial derivatives in Polar-coordinates
Related to page 819 prob 4 in this book. I am incorrectly calculating the left-hand-side (def. LHS), some newbie error with commutativity probably. Ideas?
Errors?
I propose ...
2
votes
0answers
411 views
Explain Triangle perimeter in polar coordinates
The question is to give a formula in $x$ and $y$ that gives all three sides of an equilateral triangle. The formula should not be true for points that are not part of the perimeter of the triangle. ...
2
votes
2answers
147 views
How do I find the limit of $\frac{xy\sqrt{|xy|}}{x^2 + xy + y^2}$ as x and y approach zero?
I am trying to find: $$\lim_{(x,y)\to (0,0)}\frac{xy\sqrt{|xy|}}{x^2 + xy + y^2}$$
I suspect that the limit does exist as the combined power of $x$ and $y$ is higher in the numerator than in the ...
2
votes
1answer
856 views
Horizontal and vertical asymptotes of polar curve $r = \theta/(\pi - \theta) \, , \, \in[0,\pi]$
I as supposed to find the vertical and horizontal asymptotes to the polar curve
$$ r = \frac{\theta}{\pi - \theta} \quad \theta \in [0,\pi]$$
The usual method here is to multiply by $\cos$ and ...
1
vote
2answers
221 views
Trying to plot these points in a polar coordinate system
I started with:
inside $r_1=5 \sin(θ)$ and outside $r_2=2+\sin(θ)$ and was told to sketch curve in the same polar coordinate system
I first set both equal to $0$ and solved to get $\pi$, $2\pi$, and ...
2
votes
2answers
400 views
Did I sketch this polar curve correctly?
The equation is:
$r^2=-4 \sin(2\theta)$
I first made a reference graph in cartesian coordinates using values $\displaystyle \frac{\pi}{4}$, $\displaystyle \frac{\pi}{2}$, $\displaystyle \frac{3 ...
1
vote
2answers
143 views
Sketching a polar curve
Continued off the question I asked earlier, I also have to sketch the curve.
$r^2=−4\sin(2\theta)$
So I have to set up a table of values I'm assuming. How do I know what values to choose for ...
1
vote
2answers
179 views
How to solve a polar equation when $r$ is $r^2$ instead?
I have $r^2=-4\sinθ$
and I'm asked to set $r=0$, then find θ. If I just set $r^2=0$ then I'll get $\sin(2θ)=0$. That doesn't seem right.
Then I'm asked to set $θ=0$ and then find $r$. If I use the ...
2
votes
1answer
223 views
Problem calculating an integral over a surface
I've been trying to solve this for awhile and can't find a way.
Given $ S={(x,y,z) \in R^3 : z = x^2 - y^2 , x^2 + y^2 \leq 1 } $ and $\phi :R^3 \to R $ defined as $\phi (x,y,z)= (4z +8y^2 + ...
6
votes
2answers
240 views
Need help with Curves and parameterizations
I'm having some trouble solving a couple of problems:
I know this one must be pretty easy but can't find the way to solve it.
I need to find the arc length of a curve described by $ r=1- ...
1
vote
2answers
105 views
What is a good way to pick points for polar equations?
If I want to plot $r = 4\sin3\theta$ what is a good way to pick points? The period is $2\pi/3$ so it will repeat after that, but how do I pick points so that I get a good range of values so that I ...
4
votes
2answers
728 views
Finding the volume of water in a swimming pool
Reposting from stackoverflow :) - Told to go here :)
So I've got a issue with a math assignment, and I were hoping someone could at least point me to what I should be doing, because currently I'm ...
