Express the following in terms of \( k \) if \( \tan (16)=k \) \( -\tan (376)-2 \)

To tackle this expression, we can start by simplifying \( \tan(376^\circ) \). We know that \( \tan(x) \) has a periodicity of \( 180^\circ \). So, we can reduce \( 376^\circ \) by subtracting \( 360^\circ \) (a full circle) to get \( 16^\circ \): \[ \tan(376^\circ) = \tan(376^\circ - 360^\circ) = \tan(16^\circ). \] Since \( \tan(16^\circ) = k \), we have \( \tan(376^\circ) = k \). Now, substituting this back into the expression we need to evaluate: \[ -\tan(376^\circ) - 2 = -k - 2. \] Thus, the expression in terms of \( k \) is: \[ -k - 2. \]