Mathematics Stack Exchange
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Questions tagged [parametric]

For questions about parametric equations, their application, equivalence to other equation types and definition.

In mathematics, a parametric equation of a curve is a representation of this curve through equations expressing the coordinates of the points of the curve as functions of a variable called a parameter. This contrasts with implicit equations that define a curve as the zero set of some equation in the coordinates.

The parametric forms of curves are well-suited for drawing on a computer, while their corresponding implicit forms are useful for analytic manipulations (intersections, etc.)

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Solving Parametric Equation: Multiple coefficients of trigonomic functions

How can I solve: $ x = 16 \sin^3(t) \\ y = 13\cos(t) - 5\cos(2t) - 2\cos(3t) - \cos(4t) $ I've derived $t = arcsin(\frac{x^\frac{1}{3}}{16^\frac{1}{3}})$ from the first equation but I am still unsure as to whether or not this is correct. I believe…
Kian
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Find all real numbers a such that equation 3^(x2+2ax+4a−3)−2=|(a−2)/(x+2)| Has exactly two different roots x1,x2 those belong to [−4;0]

Find all real numbers $a$ such that equation $${3^{(x^2+2ax+4a-3)}}-2=|{a-2 \over x+2}|$$ Has exactly two different roots $x_1,x_2 $ those belong to $[-4;0]$ Tried plenty different things to solve: Analyzing the quadratic equation discriminant…
user186421
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Equation of the Tangent Line and Area of Parametric Equation

I need to find the equation of the tangent line to the point (1,0) for the equation: $x=e^{-0.1t}cos(t) \\ y=e^{-0.1t}sin(t)$ I also need to calculate the area in the first quadrant bounded on the outside by the curve for $t$ greater than or equal…
FofX
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When is $x=sin(at), y=sin(bt)$ symmetric to x and y axes?

Take the simple system of parametric equations, $$x=\sin(at)$$ $$y=\sin(bt)$$ where $a,b \in \Bbb{N}$. When is this curve symmetric with respect to both the $x$ and $y$ axes? In other words, what values of $a$ and $b$ satisfy the condition that…
Zach W
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curve with vanishing tangent vector assumption

I am just reviewing some assumptions in Parametric representations The book says we assume 3-d curve has non-vanishing tangent vector. Why do we need to assume this Simply if we take $R^3$ then assume $x=f(t), y=g(t), z=h(t)$ clearly the tangent…
Mr. Math
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Parametric equations of a cycloid

Given a parametric equation of a cycloid ($t \in R$): $$ x(t)=r(t-\sin(t)); \\ y(t)=r(1-\cos(t)). $$ A vector $v=(x'(t),y'(t))$ if is not equals to zero then is a tangent vector to the curve at $(x(t),y(t))$. Given that $||v||$ is a vector norm and…
ys wong
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How would I parametrise a straight line?

If I want to parameterise a straight line and I have the equation, eg $y=2x+1$ and I also have two co-ordinates it passes through, would it ok to use the co-ordinates to parameterise in terms of $t$?
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Solving a complex exponential / logarithmic equation

I've found this interesting equation on the web: $$p-1 = (1 - e^{\alpha-\beta t})^{t+1}$$ which has to be solved for t, considering that the parameters: $\alpha, \beta, p$ are defined correctly. First thought was to use some…
Alexandru Dinu
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Is there a parametric form for a degenerate conic section?

With parametric form I mean a parametrization like $(\cos{t}, \sin{t})$ for a circle. A conic section has such a parametrization, but suppose it degenerates in 2 lines (ranges of points), is there a parametrization that goes from $-\infty$ to…
Gerard
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Parameterization of the negative half of the y-axis

I need to parameterize the negative half of the y-axis in spherical and cylindrical coordinates. I know what spherical and cylindrical coordinates are, just not sure where to start to parameterize the negative half of the y-axis
William Carey
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Parametric Function for Coloring

I'm trying to write a parametric straightline function that changes its values between 0.529 and 0.933. Usually what I would do is: $r = 0.529+(0.933-0.529)*v$ where parameter $v= [0,1]$ This ensure that my r value will either be 0.529 or…
KillerKidz
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Parametrization Semicircle On Sphere

I need to find a parametrisation in terms of $t$ for a half circle on a sphere with radius $R$. The circle goes from $(R,0,0)$ to $(-R,0,0)$ and is going through the point $(0, R/\sqrt{2},R/\sqrt{2})$. I was thinking about putting the sphere in…
user112167
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eliminate parametric parameter to determine the Cartesian equation.

$$x = \sin^2(t), y = \cos(t)$$ I know that to eliminate parameter involving $\sin$ and $\cos$, we should reduce it to $x^2 + y^2 = r^2$. So, $x^2 = \sin^4(t)$, $y^2 = \cos^2(t)$ But I can't make $\sin^4(t)$ and $\cos^2(t)$ to $1$. Any tips?
Joshua
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Removing parameter $t$ from $z$-axis

How do I remove the parameter $t$ from the $z$-function in the following: $$\begin{align}x&=a\cos{t}-a\\ y&=a\sin{t}\\ z&=nt\end{align}$$ (where $n,a$ are arbitrary coefficients) So far I have: $$\begin{align} x&=(a^2-y^2)^{0.5} - a\\ y&=(a^2…
arnie
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Parametrizing curve with not only one peak

I obtained experimental data (thermal analysis) and need to parametrize the resulted curves for modeling. An example of two curves obtained: I tried to use a Weibull distribution, but since I have two peaks, it seems that I need something bimodal.…
Shukoff
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