Parametric Curves: Finding Tangents at (0,0) Using Lissajous Figure Equations

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In summary, the conversation is about a problem involving a Lissajous figure and its parametric equations. The person is seeking urgent help to find the equations for the two tangents at the point (0,0). They have found the slope to be -sint/cos(2t)*2, but are unsure of how to proceed. Someone suggests that the tangents occur at t = pi/2 and -pi/2, with corresponding slopes of 1/2 and -1/2. Further help is requested from anyone who can provide it. The website spacetime is also mentioned as a resource for physics.
  • #1
ziddy83
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URGENT help needed please...

I have been having problems with this problem...it says...
A graph of the Lissajous figure is given by the paraetric equations:

x=sin2t and y=cost

Show that the curve has two tangents at the point (0,0) and find their equations

Can someone please help me? I've been trying to figure this out for the past two days. I got the slope to be

-sint/cos(2t)*2 I am not sure where to go from there...so please..if anyone can help that would be fantastic. :confused:
 
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anyone...??
 
  • #3
Origin means x=y=0. They are zero for t = pi/2 and -pi/2. For these you get two values of the slope, 1/2 and -1/2.


spacetime
www.geocities.com/physics_all
 

FAQ: Parametric Curves: Finding Tangents at (0,0) Using Lissajous Figure Equations

What are parametric curves and how are they different from regular curves?

Parametric curves are a type of mathematical function that describes the relationship between two variables in terms of a third independent variable. This means that the x and y coordinates of a point on the curve are both expressed as equations involving a third variable, typically denoted as t. This is different from regular curves, where the x and y coordinates are defined explicitly in terms of one another.

How are parametric curves used in science and engineering?

Parametric curves are used in a variety of scientific and engineering applications, such as in the design of computer graphics, modeling of physical systems, and data analysis. They are particularly useful in cases where the relationship between two variables is not easily described by a single equation, and can provide a more accurate representation of a system or phenomenon.

What are the advantages of using parametric curves over regular curves?

One key advantage of parametric curves is their ability to describe complex and nonlinear relationships between variables. They also allow for more flexibility in representing curves, as the third variable t can be used to manipulate the curve in a variety of ways. Additionally, parametric curves can often be easier to work with and analyze mathematically compared to regular curves.

Are there any limitations to using parametric curves?

While parametric curves have many advantages, they also have some limitations. One limitation is that they may not always be as intuitive to understand as regular curves, as the relationship between the variables is not always immediately apparent. Additionally, parametric curves can be more computationally intensive to work with, which can make them less practical for certain applications.

How can parametric curves be visualized and graphed?

Parametric curves can be graphed using parametric equations, where the x and y coordinates of points on the curve are expressed in terms of t. Another way to visualize parametric curves is by plotting a series of points on the curve using different values of t and connecting them with a smooth line. Additionally, computer programs and graphing calculators often have features that allow for the graphing of parametric curves.

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