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## Homework Statement

Parametric equations and a parameter interval for the motion of a particle in the xy-plane are given. Identify the particle's path by finding a Cartesian equation for it. Graph the Cartesian equation. Indicate the portion of the graph traced by the particle and the direction of motion.

x = 2 sin t, y = 4 cos t, 0 ≤ t ≤ 2π

## Homework Equations

##cos^2t + sin^2t=1##

## The Attempt at a Solution

## x= 2 sin t ##

## y = 4 cos t ##

Square both sides :

## \frac{x^2}{4} = sin t^2 ##

## \frac{y^2}{16} = cos^2 t ##

Add the two equations :

## \frac{y^2}{16} + \frac{x^2}{4} = 1 ##

This equation forms an ellipse.

When t = 0 , x = 0 and y = 4

When t = ##2\pi## , x = 0 and y = 4

Counterclockwise from (0,4) to (0,4) , one rotation .

Could someone check my answer ?