#### Answer

$y=\sin{(x-2)}$ means the function involves the sine value of the expression $(x-2)$, while the original given $y=\sin{x}-2$ means $2$ will be subtracted from the sine value of $x$.

#### Work Step by Step

The student was wrong because $y=\sin{(x-2)}$ means the function involves the sine value of the expression $(x-2)$, while the original given $y=\sin{x}-2$ means $2$ will be subtracted from the sine value of $x$.