2
votes
1answer
39 views

Parametric & Trigonometry

$$x=7\sin(t)+\sin(7t)$$ $$y=7\cos(t)+\cos(7t)$$ How would I solve this one out? I have to simplify the two enough to graph it. I squaring the two and adding them together, but I hit a roadblock: ...
0
votes
0answers
44 views

Analytical Models for Hysteresis of Complicated Systems

I’ve been working with a system that exhibits hysteresis and I’ve found that the more common models do not work for me. I am wondering if anyone is aware of other models that might be out there for ...
0
votes
1answer
56 views

Parametric Equation of sine wave helically wrapped around a cylinder

I want a parametric equation of a sine wave at a small ramp angle wrapped around a cylindrical body (3D). The parametric equation below gets me close to what I'm looking for, but not quite since the ...
0
votes
1answer
35 views

Prove the normal will be at constant distance form origin in this parametric function?

Given a function, $x = a(cos \theta + \theta \sin\theta])$, $y = a(sin\theta - \theta\ cos\theta)$, $a \in R$ Prove that the normal drawn on each point is at constant distance form the origin? If ...
1
vote
0answers
44 views

Relation between $\sin(t)$($\cos(t)$) and $\sin(at)$ ($\cos(at)$) when both are rational

This question relates to Parametric equations where sin(t) and cos(t) must be rational. Suppose it is given that $\cos(t)$ and $\sin(t)$ are both rational and also $\cos(at)$ and $\sin(at)$, where ...
2
votes
1answer
33 views

$2\pi^2(x-1)^2+4a\cos(2\pi x)-9a^3=0$ For which $a$ has only one solution…

For which values of real parameter $a$ the following equation has only one solution: $$2\pi^2(x-1)^2+4a\cos(2\pi x)-9a^3=0$$ Frankly I have no idea and I hope you'll give me some understandable hint ...
1
vote
2answers
42 views

Find the point on an ellipse by angle.

How do I find the point on the ellipses at 45'. I found this, which answers part of it, but I need to know how to calculate for (x,y) at 45'. I could also use a good explanation for the ...
1
vote
1answer
39 views

What is being represented by this 2 images?

image 1 image 2 It's possible that image 1 is showing some kind of methods for building polygons out of trigonometric functions ? It's also possible that image 2 is a quadratic bezier curve ?
0
votes
0answers
32 views

Inverse ease-in-out parametric function

I'm trying to create an inverse ease-in-out function that given values from 0 to 1, produces values from 0 to 1. Opposite of a typical ease-in-out function, though, I want it to start accelerated, ...
1
vote
1answer
244 views

Coordinate of intersection between line and square

TL;DR given a square and a point $p$, I need the intersection between the perimeter of the square and a ray cast from the center of the square through point $p$. This is my approach so far, but I will ...
4
votes
2answers
489 views

Parametric equations of cycloid on a Ramp

A small wheel of radius r is situated at the top of a ramp having an angle θ = π/3 rad as it appears in the figure below. At t = 0 the wheel is at rest and then it starts to rotate clockwise in the ...
0
votes
1answer
317 views

Find equation of tangent line

Find the equation of the tangent line at parameter values $\theta=\pi/6$ and $\theta =5\pi/4$ to the cycloid given by $$x(t)=r\theta-r\sin \theta$$ and $$y(t)= r-r\cos \theta$$ with $\theta\in ...
0
votes
0answers
16 views

Parametrically defined Spheres in $R^n$

So I have 2 questions here which are closely linked: How do you parametrically define the circle $(x')^2 + (y')^2 = r^2$ using (x') and (y') as coordinates on the plane ax + by + cz = 0 that are ...
1
vote
3answers
179 views

Equation of a Circle from parametric functions of sin and cos

Given: x = 2 cos (t/2) y = 2 sin (t/2) How do we find the equation of the circle? I know that x^2 + y^2 = 1, where x = cos(t) y = sin(t) so x^2 = (2 cos (t/2))^2 y^2 = (2 sin (t/2))^2 How do ...
1
vote
0answers
95 views

Splitting parametric curve equation into two ranges

I am examining the speed of motion on curves and in the textbook i am reading , the example was showing that using a parametric equation for an ellipse will result in a regular motion (as expected) , ...
3
votes
2answers
72 views

Why do we need to find the intersection between these lines?

We have the functions $$ x = -1 + 2 \cos(t)$$ $$ y = 3 + 2 \sin(t)$$ They give P's orbit with $t$ on $\left[0, \dfrac{3}{2} \pi\right]$ Find (to 2 decimal places accurate) for which values of t ...
0
votes
0answers
72 views

Torus equation in terms of tangent

So if I have an equation for a torus in $F(a,b) = (X, Y, Z)$ where $X = (R + r\cos a)\cos b$ and $0 < r < R$, how would I go about rewriting this equation for $X$ in terms of $\tan(a/2)$ and ...
3
votes
1answer
317 views

How are the parametric equations describing the cupid curve derived? [duplicate]

No doubt as some people have already seen, today morning wolfram posted the best valentine ever. The graph depicting cupid with its arrow and floating hearts around it involves something like 6 pages ...
2
votes
2answers
110 views

Converting $x = \sin \frac{t}{2}, y = \cos \frac{t}{2}$ to Cartesian form

How can we transform these parametric equations to Cartesian form? $$x = \sin \frac{t}{2}, \quad y = \cos \frac{t}{2}, \quad -\pi \leq t \leq \pi.$$
1
vote
1answer
229 views

Arc Length Of Parametric Curve

I attached the problem as a file: Where did the trig functions go? I sifted through the different trig identities and formulas, but couldn't find anything that I could use. What should I do?
1
vote
1answer
142 views

Restriction Of Parametric Functions Domain

The problem I am working on is, "Sketch the curve represented by the parametric equations (indicate the orientation of the curve), and write the corresponding rectangular equation by eliminating the ...
1
vote
1answer
434 views

Parameterize a straight line using polar coordinates… without angle.

I had to parameterize a straight line with starting point in $A=(-3,7)\\ $ and endpoint in $B=(4,1)$. My idea was to use the equation for the line that goes through two points. That is: $$ \frac { ...
35
votes
3answers
2k views

Do “Parabolic Trigonometric Functions” exist?

The parametric equation $$\begin{align*} x(t) &= \cos t\\ y(t) &= \sin t \end{align*}$$ traces the unit circle centered at the origin ($x^2+y^2=1$). Similarly, $$\begin{align*} x(t) ...
1
vote
1answer
522 views

Solve x = sin(t) for t

How can I solve: $(\frac{x}{16})^{\frac{1}{3}} = \sin(t)$ for t?
2
votes
1answer
181 views

Finding Angle of Elevation to hit X, Y

My ultimate goal is to find the angle of elevation necessary to launch a projectile from the origin to (x,y) with initial velocity V and under gravitational acceleration g. Wind resistance is ignored. ...