stau40 said:Homework Statement
Find the length of the path over (2 cos t - cos 2t, 2 sin t - sin 2t) 0<=t<=(pi/2)
Homework Equations
sin^(2) x = (1-cos 2x)/2
The Attempt at a Solution
I have worked my way thru the problem and I have arrived at 2 (sq root 2) antiderivative (sq root (1-cos t)), but I'm not sure how this coverts into the relevant equation above? Thanks in advance!
A parametric equation is a mathematical expression that defines a set of coordinates in terms of one or more parameters. These equations are commonly used to represent curves, surfaces, and other mathematical objects.
To write a parametric equation, you must first identify the parameters that will be used in the equation. Then, you can use these parameters to define the x and y coordinates in terms of a variable t, typically representing time. For example, a simple parametric equation for a circle would be x = r cos(t), y = r sin(t), where r is the radius of the circle.
Parametric equations allow for more complex and accurate representations of mathematical objects, such as curves and surfaces, compared to traditional equations. They also allow for greater flexibility in manipulating and graphing these objects.
Parametric equations are used in a variety of fields, including physics, engineering, and computer graphics. Some common applications include modeling the motion of objects, designing curves and surfaces in 3D modeling, and creating visual effects in video games and animation.
To graph a parametric equation, you can plot a series of points by substituting different values for the parameter t. Alternatively, you can use a graphing calculator or computer software to plot the equation and visualize the resulting curve or surface. It is also important to choose an appropriate range of values for t to ensure that the entire curve is displayed.