# Tagged Questions

2answers
115 views

### Plotting a polar curve

The question is, to generate a polar graph using a graphing utility, and to choose parameter interval so that the complete graph is generated. $$r=\cos\frac{\theta}{5}$$ To find such an interval, we ...
5answers
119 views

### Points on $(x^2 + y^2)^2 = 2x^2 - 2y^2$ with slope of $1$

Let the curve in the plane defined by the equation: $(x^2 + y^2)^2 = 2x^2 - 2y^2$ How can i graph the curve in the plane and determine the points of the curve where $\frac{dy}{dx} = 1$. My work: ...
1answer
70 views

### Drawing polar graphs when given theta in terms of the radius

I know how to plot when it is like $r=10 \cdot \sin(2\theta)$. But how to do that when the condition is like: $\theta =2 \pi \cdot \sin(r)$?
1answer
36 views

### What is the area of the closed curve?

The graph of the polar graph $r=\dfrac{4}{2-\cos\theta}$ forms a closed curve. Find the area of the region inside the curve.
2answers
5k views

### Cannabis Equation

How can an equation for the following curve be derived? $$r=(1+0.9 \cos(8 \theta)) (1+0.1 \cos(24 \theta)) (0.9+0.1 \cos(200 \theta)) (1+\sin(\theta))$$ (From WolframAlpha)
2answers
102 views

### Ampersand curve in polar coordinates

I got an assignment to write a program which draws the ampersand curve. The equation of ampersand curve looks like this: $(y^2-x^2)(x-1)(2x-3)=4(x^2+y^2-2x)^2$ I was given an advice to convert this ...
0answers
161 views

### How to plot a stream function

This question relates to fluid mechanics and I have the components in polar coordinates. The components of the velocity field are; $$v_r= \frac{-kr}{z}$$ $$v_z= kz$$ $$v_\theta= 0$$ and I have ...
2answers
613 views

### Sketch $r=\cos(5 \theta)$? $r$ as a function of $\theta$ in cartesian coordinates

I think I have to plug in numbers into $\theta$ such as 0 and $\pi/6$. What kind of numbers should I plug in ? Sketch $r=\cos(5 \theta)$? $r$ as a function of $\theta$ in cartesian coordinates
2answers
290 views

### Equation of circular sine waves in the water

I have to write the equation of a sine wave expanding circularly from a point $P_0=(x_0,y_0)$. The wave has the form $\eta(\rho)=A\sin(\omega\rho)$ where $\rho$ is the distance from the point $P_0$. ...
1answer
162 views

### Defining a spiral in polar coordinates

I'm trying to find a general form for a spiral that fits the following criteria: the inner radius is $N$, and for any point $q$ on the spiral, the arc length from the start of the spiral to $q$ is ...
2answers
2k views

### Plotting in the Complex Plane

I just wonder how do you plot a function on the complex plane? For example,$$f(z)=\left|\dfrac{1}{z}\right|$$ What is the difference plotting this function in the complex plane or real plane?
1answer
167 views

### equation for the region inside a circle

What equation or group of equations fill the entire or part of a region inside a circle without using inequalities? Update I don't know if this problem is already solved, I'm trying to find the ...
1answer
1k views

### General Cartesian/Rectangular Equation for Polar Rose ($r=\sin(k\theta)$)

How do I convert the Polar Equation $r=\sin(k \theta)$ to Cartesian Equation? I understand that $r^2=x^2+y^2$ and that $x=r\cos\theta$ and $y=r\sin\theta$, but no matter how I try to arrange them it ...
1answer
234 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 ...
3answers
2k views

### Argand Diagram - Quadrants help

I forgot the rules of adding angles when it comes to argand diagrams. In the first quadrant, you add 90 degrees to whatever angle you get, what about Q2 Q3 Q4 ? This picture will explain what i mean ...
3answers
125 views

### Converting a polar coord to the range $0\le\theta\le2\pi?$

I know that you can keep adding/subtracting numbers to a polar coord, but what if I want to be able to take a number and just convert it to its positive equivalent?