help needed w/ math question

Question

A pair of parametric equations is given below.

x = 4 sin(t),  y = 4 cos(t), 0 ≤ t ≤ 𝜋

Find a rectangular-coordinate equation for the curve by eliminating the parameter.

My answer is y=sqrt ((4+x)(4-x)) but it is incorrect.

Answer 1

x / 4 = sin t

x² / 16 = sin² t

x² / 16 = 1 - cos² t

y / 4 = cos t

y² / 16 = cos² t

x² / 16 = 1 - (y² / 16)

(x² / 16) + (y² / 16) = 1

x² + y² = 16

Same result if sin was substituted for cos