Intereting Posts

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Every set of $n$ generators is a basis for $A^{n}$
Prove that $x^4+x^3+x^2+x+1 \mid x^{4n}+x^{3n}+x^{2n}+x^n+1$
Proving that $T_t := S_t -\left| x \right| -\frac {n-1}{2} \int _0 ^t \frac {1}{S_u}~du$ is a brownian motion
$E'$ is closed, where $E'$ is the set of limit points of $E$
In which sense does Cauchy-Riemann equations link complex- and real analysis?
Determine convergence of the series $\sum_{n=1}^{\infty}\frac{(2n-1)!!}{(2n)!!}$
show this inequality $3^{\frac{n}{4}}\cdot (3^{\frac{1}{4}}-1)^{8-n}\le 1+n$
About the Legendre differential equation
If a measure only assumes values 0 or 1, is it a Dirac's delta?
Let $L_p$ be the complete, separable space with $p>0$.
Poincare duality in group (co)homology
Problem 4.3, I. Martin Isaacs' Character Theory
Overlapping Probability in Minesweeper
If $N=q^k n^2$ is an odd perfect number and $q = k$, why does this bound not imply $q > 5$?

Consider a sine wave having $4$ cycles wrapped around a circle of radius 1 unit (its center needs not be the origin of a Cartesian coordinate system). Assume that the length of axis of the sine wave is as same as the circumference of the circle.

The circumference of circle is assumed to be mapped to $2\pi\ \mathrm{rad}$. Therefore, the sine wave represents the equation along the $x$-axis:

$$ y = \sin(4x) $$

- Why is the area of a circle not $2 \pi R^2$?
- Recurrent points and rotation number
- How to calculate the inverse of a point with respect to a circle?
- Area of Shaded Region
- Four complex numbers $z_1,z_2,z_3,z_4$ lie on a generalized circle if and only if they have a real cross ratio $\in\mathbb{R}$
- Two circles intersection

To find the equation of the sine wave with the circumference of circle acting as the $x$-axis, one approach is to consider the sine wave along a rotated line like aligned $\frac\pi4\ \mathrm{rad}$ to $x$-axis. But it doesn’t suffice for the circular path. This is where the problem of finding the equation is stuck. A hint/help taking to a right answer would be appreciated.

For more clarity, here is a rough image. In the image, four lines are drawn to clearly distinguish between crests and troughs.

- How do you calculate this limit $\mathop {\lim }\limits_{x \to 0} \frac{{\sin (\sin x)}}{x}$?
- Finding square roots of $\sqrt 3 +3i$
- Proving $\cot(A)\cot(B)+\cot(B)\cot(C)+\cot(C)\cot(A)=1$
- Prove that $\prod_{k=0}^{n-1}\sin \left( x + k\frac{\pi}{n} \right) = \frac{\sin nx}{2^{n - 1}}$
- Verify $\int\sec x\ dx=\frac12 \ln \left\lvert\frac{1+\sin x}{1-\sin x}\right\rvert + C$
- How were the sine, cosine and tangent tables originally calculated?
- Four complex numbers $z_1,z_2,z_3,z_4$ lie on a generalized circle if and only if they have a real cross ratio $\in\mathbb{R}$
- How to find the equation of a line tangent a circle and a given point outside of the circle
- Integral $\int_0^{\pi/2}\arctan^2\left(\frac{6\sin x}{3+\cos 2x}\right)\mathrm dx$
- Explaining $\cos^\infty$

Do it first for the circle centered at the origin in polar coordinates.

Then switch do Cartesian coordinates, then shift to the actual center of the circle.

it should be, in cartesian coordinates

x = (R + a · sin(n·θ)) · cos(θ) + xc

y = (R + a · sin(n·θ)) · sin(θ) + yc

where

R is circle’s radius

a is sinusoid amplitude

θ is the parameter (angle), from 0 to 2π

xc,yc is circle’s center point

n is number of sinusoids on circle

you can also get a pure cartesian equation (non-parametric) on x/y, but just for half circle, solving second for sin(θ) and replacing it on first one.

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- How can we calculate the limit $\lim_{x \to +\infty} e^{-ax} \int_0^x e^{at}b(t)dt$?
- Cardinality of the set of all real functions of real variable
- Can I switch to polar coordinates if my function has complex poles?
- If $a+b+c=3$ show $a^2+b^2+c^2 \leq (27-15\sqrt{3})\left(\frac{1}{a}+\frac{1}{b}+\frac{1}{c}\right)$
- Palindromic Numbers – Fractal or Chaotic?
- Category of binomial rings
- Extensions of Ramanujan's Cos/Cosh Identity
- How many roots have modulus less than $1$?