tan π 6 = sin π 6 cos π 6 = 1 2 3 2 = ( 1 2 ) 2 3 = 1 3 = 3 3 {\displaystyle \tan {\frac {\pi }{6}}={\frac {\sin {\frac {\pi }{6}}}{\cos {\frac {\pi }{6}}}}={\frac {\frac {1}{2}}{\frac {\sqrt {3}}{2}}}=\left({\frac {1}{2}}\right){\frac {2}{\sqrt {3}}}={\frac {1}{\sqrt {3}}}={\frac {\sqrt {3}}{3}}}
tan π 4 = sin π 4 c o s π 4 = ( 2 2 ) 2 2 = 1 {\displaystyle \tan {\frac {\pi }{4}}={\frac {\sin {\frac {\pi }{4}}}{cos{\frac {\pi }{4}}}}=\left({\frac {\sqrt {2}}{2}}\right){\frac {2}{\sqrt {2}}}=1}
tan π 3 = sin π 3 c o s π 3 = ( 3 2 ) 2 1 = 3 {\displaystyle \tan {\frac {\pi }{3}}={\frac {\sin {\frac {\pi }{3}}}{cos{\frac {\pi }{3}}}}=\left({\frac {\sqrt {3}}{2}}\right){\frac {2}{1}}={\sqrt {3}}}