For each parametrization find a value of t for which x(t) = (1, 0), then find the next greater value of t for which x(t) = (0, 1) .vanitymdl said:
The purpose of parameterization of the circle is to represent points on a circle using parameters or variables. This allows for easier calculations and analysis of the circle's properties.
The circle can be parameterized using either Cartesian coordinates or polar coordinates. In Cartesian coordinates, the circle can be represented as (x,y) where x = r cos θ and y = r sin θ. In polar coordinates, the circle can be represented as (r,θ) where r is the radius and θ is the angle measured from the positive x-axis.
The equation for parameterization of the circle is x = r cos θ and y = r sin θ, where r is the radius and θ is the angle measured from the positive x-axis.
Parameterization of the circle allows for easier calculations and graphing of the circle's properties. It also allows for the representation of a point on the circle using only two variables, making it more efficient.
Parameterization of the circle is used in various fields such as physics, engineering, and computer graphics. It is used to model circular motion, calculate forces acting on a circular object, and create 3D circular shapes in computer graphics.