Determine the value \( \quad-\tan (420) \) give your answe is surd form

1. Recognize that the tangent function has a period of \(360^\circ\). Therefore, we can subtract \(360^\circ\) from \(420^\circ\) to find an equivalent angle: \[ 420^\circ - 360^\circ = 60^\circ \] Thus, \[ \tan(420^\circ) = \tan(60^\circ) \] 2. We know that: \[ \tan(60^\circ) = \sqrt{3} \] 3. The original expression is: \[ -\tan(420^\circ) \] Substituting the value from step 2 gives: \[ -\tan(420^\circ) = -\sqrt{3} \] The final answer in surd form is \(-\sqrt{3}\).