Find an Equation of Y as a Function of X $$x = 2 \sin t , \quad y = 2 \cos t , \quad t \in [ 0,2 \pi ]$$

Multiple Choice

Find an equation of y as a function of x for the parametric equations given below by eliminating the parameter. Also, indicate the direction of the curve. $$x = 2 \sin t , \quad y = 2 \cos t , \quad t \in [ 0,2 \pi ]$$

A) $x ^ { 2 } + y ^ { 2 } = 2 , \quad \text { clockwise }$
B) $x ^ { 2 } + y ^ { 2 } = 2 , \quad \text { counterclockwise }$
C) $x ^ { 2 } + y ^ { 2 } = 4 , \quad \text { clockwise }$
D) $x ^ { 2 } + y ^ { 2 } = 4 , \quad \text { counterclockwise }$