# How do you find the exact values of the six trig functions of angle 120?

How do you find the exact values of the six trig functions of angle 120?
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Lorenzo Acosta
$\mathrm{sin}{120}^{\circ }=\mathrm{sin}\left({180}^{\circ -{60}^{\circ }}\right)=\mathrm{sin}{60}^{\circ }=\frac{\sqrt{3}}{2}$
$\mathrm{cos}{120}^{\circ }=\mathrm{cos}\left({180}^{\circ }-{60}^{\circ }\right)=-\mathrm{cos}{60}^{\circ }=-\frac{1}{2}$
$\mathrm{tan}{120}^{\circ }=\mathrm{tan}\left({180}^{\circ }-{60}^{\circ }\right)=-\mathrm{tan}{60}^{\circ }=-\sqrt{3}$
$\mathrm{cos}ec{120}^{\circ }=\mathrm{cos}ec\left({180}^{\circ }-{60}^{\circ }\right)=\mathrm{cos}ec{60}^{\circ }=\frac{2}{\sqrt{3}}$
$\mathrm{sec}{120}^{\circ }=\mathrm{sec}\left({180}^{\circ }-{60}^{\circ }\right)=-\mathrm{sec}{60}^{\circ }=-2$
$\mathrm{cot}{120}^{\circ }=\mathrm{cot}\left({180}^{\circ }-{60}^{\circ }\right)=-\mathrm{cot}{60}^{\circ }=-\frac{1}{\sqrt{3}}$