Final answer:
The question seems to refer to the process of eliminating the parameter in a pair of parametric equations to find a Cartesian equation of a curve, typically involving trigonometric identities.
Step-by-step explanation:
The question seems to refer to the process of eliminating the parameter in a pair of parametric equations to find a Cartesian equation of a curve, typically involving trigonometric identities. For a complete pair of equations like x = 2cos(θ) and y = 2sin(θ), we could use the Pythagorean identity to derive x^2 + y^2 = 4, representing a circle. To eliminate the parameter and find a Cartesian equation of the curve when given x=2cos(θ), we can use trigonometric identities to express the equation in terms of x and y without the parameter θ.
However, the given equation seems incomplete as typically, a parametric equation for a curve in the plane will have two equations: one for x and one for y, such as x = 2cos(θ) and y = 2sin(θ) or similar. Assuming we had a second equation, we could use the Pythagorean identity sin^2(θ) + cos^2(θ) = 1 to eliminate the parameter. For example, if y is given by y=2sin(θ), we could write y^2 + x^2 = (2sin(θ))^2 + (2cos(θ))^2 = 4(sin^2(θ) + cos^2(θ)) = 4, which simplifies to the Cartesian equation x^2 + y^2 = 4, which represents a circle with a radius of 2 centered at the origin.