Sketch Parametric Curve and Find Cartesian Equation

In summary, a parametric curve is a mathematical concept that represents a curve in terms of parameters. To sketch a parametric curve, you plot points using the coordinates determined by the parameter(s) and connect them. A Cartesian equation is an equation that describes a curve in terms of x and y coordinates, and can be used to represent complex shapes and curves. To find the Cartesian equation of a parametric curve, the parameters must be eliminated from the equations. Parametric curves and Cartesian equations have various applications in fields such as science, engineering, and design. They are also important in studying motion and trajectories.
  • #1
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sketch the parametric curve and eliminate the parameter to find the cartesian equation of the curve $x=\cos\left({\theta}\right)$, $y=\sec\left({\theta}\right)$, $0\le \theta < \pi/2$

$y=\frac{1}{\cos\left({\theta}\right)}=\frac{1}{x}$

i sketched the curve. how do i do the second part?
 
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  • #2
You've already eliminated the parameter when you wrote:

\(\displaystyle y=\frac{1}{\cos(\theta)}=\frac{1}{x}\)
 
  • #3
oh. wow I am really stupid. hahaha thanks (Tongueout)
 

FAQ: Sketch Parametric Curve and Find Cartesian Equation

What is a parametric curve?

A parametric curve is a mathematical concept that represents a curve in terms of one or more parameters. These parameters are typically represented by variables such as t or u, and they determine the coordinates of points along the curve.

How do you sketch a parametric curve?

To sketch a parametric curve, you will need to plot points using the coordinates determined by the parameter(s). Then, connect the points to create a smooth curve. You can also use a graphing calculator or computer software to plot the curve.

What is a Cartesian equation?

A Cartesian equation is an equation that describes a curve or shape in terms of x and y coordinates. It is written in the form y = f(x), where f(x) is a function of x. This type of equation is used to represent curves that are not easily described by a single equation.

How do you find the Cartesian equation of a parametric curve?

To find the Cartesian equation of a parametric curve, you will need to eliminate the parameter(s) from the equations. This can be done by solving for the parameter(s) in terms of x and y and substituting them into the original equations. The resulting equation will be the Cartesian equation of the curve.

What are some applications of parametric curves and Cartesian equations?

Parametric curves and Cartesian equations are used in various fields of science and engineering, including physics, astronomy, and computer graphics. They are also commonly used in designing and modeling complex shapes and curves in architecture and product design. Additionally, they are essential in understanding and analyzing motion and trajectories in kinematics and dynamics.

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