Answer
$\sqrt{3}$
Work Step by Step
RECALL:
(1)The reference angle of a given angle is equal to the smallest acute angle that the terminal side makes with the x-axis.
(2) Based on the location of the terminal side of an angle $\theta$, the reference angle can be found using the formula:
(i) Quadrant I: $\theta$
(ii) Quadrant II: $180^0-\theta$
(iii) Quadrant III: $\theta-180^o$
(iv) Quadrant IV: $360^o-\theta$
The given angle is coterminal with $420^o-360^o=60^o$.
This angle is in Quadrant I so its reference angle is itself.
Thus,
$\tan{420^o} = \tan{60^o}$
$60^o$ is a special angle whose tangent value is $\sqrt{3}$.
Thus,
$\tan{420^o}=\tan{60^o}=\sqrt{3}$
