Find the equation of path pattern of a particle.
The particle coordinate (x,y) is given by the funtions
x = 2Sin(t) and y = 3Cos(t)

x = Sin (t)

y = Cos (t)

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SOLUTION

Sin(t) = ( x / ) equation 1
Cos (t) = ( y / ) equation 2

Formula recall
Sin²(t) + Cos²(t)= 1 , Trigonometric identity

By substitution: Cos²(t) = ( y / 3 )² and Sin²(t) = ( x / 2 )²
( x² / ) + ( y ²/ ) = 1

ANSWER, x² + y² = This is the equation of the path pattern of a particle.