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

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

UpStudy AI · Accepted Answer

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 $$-\sqrt{3}$$.
$$-\sqrt{3}$$

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

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