6.2 Trigonometric Functions: Unit Circle Approach/57

$-{\frac {\pi }{6}}=-30^{\circ }$
$360^{\circ }-30^{\circ }=330^{\circ }={\frac {\sqrt {3}}{2}},-{\frac {1}{2}}$
$cos(-{\frac {\pi }{6}})={\frac {\frac {\sqrt {3}}{2}}{\cancel {1}}}={\frac {\sqrt {3}}{2}}$
$sin(-{\frac {\pi }{6}})={\frac {-{\frac {1}{2}}}{\cancel {1}}}=-{\frac {1}{2}}$
$tan(-{\frac {\pi }{6}})={\frac {-{\frac {1}{\cancel {2}}}}{\frac {\sqrt {3}}{\cancel {2}}}}\cdot (2)=-{\frac {1}{\sqrt {3}}}\cdot ({\sqrt {3}})={\frac {-{\sqrt {3}}}{3}}$
$sec(-{\frac {\pi }{6}})={\frac {1}{\frac {\sqrt {3}}{\cancel {2}}}}\cdot (2)={\frac {2}{\sqrt {3}}}\cdot ({\sqrt {3}})={\frac {2{\sqrt {3}}}{3}}$
$csc(-{\frac {\pi }{6}})={\frac {1}{-{\frac {1}{\cancel {2}}}}}\cdot (2)={\frac {2}{-1}}=-2$
$cot(-{\frac {\pi }{6}})={\frac {\frac {\sqrt {3}}{2}}{-{\frac {1}{2}}}}\cdot (2)={\frac {\frac {2}{\sqrt {3}}}{-2}}=-{\sqrt {3}}$