Question 919009
Calculate the exact answer. No decimals.
tan((14pi)/3)
<pre>
{{{(14*pi)/3}}}______{{{(2520^o)/3}}}_____{{{840^o}}}
Reference angle of {{{840^o}}}: 840 - 360 * 2 = {{{120^o}}}

tan {{{120^o}}} is in the 2nd quadrant where sin is POSITIVE, cos is NEGATIVE, and so, tan is NEGATIVE
{{{tan 120^o = sin (120^o)/cos (120^o)}}}
{{{tan 120^o = (sqrt(3)/2)/(- 1/2)}}}
{{{tan 120^o = (sqrt(3)/2) * (- 2/1)}}}
{{{tan 120^o = (sqrt(3)/cross(2)) * (- cross(2)/1)}}}
{{{highlight_green(highlight_green(tan 120^o = tan (14*pi)/3 = - sqrt(3)))}}}