Mathematics

The key is to use the perpendicularity condition: if two lines are perpendicular, their slopes multiply to $-1$. Since $y = x - 4$ has slope $1$, the tangent line to the curve must have slope $-1$. Find where the derivative $y' = e^x(\cos x - \sin x)$ equals $-1$, then solve for $c$ numerically or by testing values.

The key is to use the perpendicularity condition: if two lines are perpendicular, their slopes multiply to $-1$. Since $y = x - 4$ has slope $1$, the tangent line to the curve must have slope $-1$. Find where the derivative $y' = e^x(\cos x - \sin x)$ equals $-1$, then solve for $c$ numerically or by testing values.