$3°$刻みで$273°～357°$のときの三角関数がどんな式になるのかをまとめてみました。
$0°<α<90°$を使って$270°<β<360°$の三角関数を表すと以下のようになります。
\begin{align*}\sin\beta&=\sin(360°-\alpha)\\[0.5em]&=-\sin\alpha\\[1em]\cos\beta&=\cos(360°-\alpha)\\[0.5em]&=\cos\alpha\\[1em]\tan\beta&=\tan(360°-\alpha)\\[0.5em]&=-\tan\alpha\end{align*}
$273°\ (=\frac{91}{60}\pi)$ $(=360°-87°)$
\begin{align*}\sin273°&=-\frac{2\sqrt{20+10\sqrt{3}+4\sqrt{5}+2\sqrt{15}}+\sqrt{2}+\sqrt{30}-\sqrt{6}-\sqrt{10}}{16}\\[1em]\cos273°&=\frac{\sqrt{30}+\sqrt{10}-\sqrt{6}-\sqrt{2}-2\sqrt{20+4\sqrt{5}-10\sqrt{3}-2\sqrt{15}}}{16}\\[1em]\tan273°&=-\frac{\sqrt{110+60\sqrt{3}+46\sqrt{5}+28\sqrt{15}}+4+3\sqrt{3}+2\sqrt{5}+\sqrt{15}}{2}\end{align*}
$276°\ (=\frac{23}{15}\pi)$ $(=360°-84°)$
\begin{align*}\sin276°&=-\frac{\sqrt{10-2\sqrt{5}}+\sqrt{3}+\sqrt{15}}{8}\\[1em]\cos276°&=\frac{\sqrt{30-6\sqrt{5}}-\sqrt{5}-1}{8}\\[1em]\tan276°&=-\frac{\sqrt{50+22\sqrt{5}}+3\sqrt{3}+\sqrt{15}}{2}\end{align*}
$279°\ (=\frac{31}{20}\pi)$ $(=360°-81°)$
\begin{align*}\sin279°&=-\frac{\sqrt{2}+\sqrt{10}+2\sqrt{5-\sqrt{5}}}{8}\\[1em]\cos279°&=\frac{\sqrt{2}+\sqrt{10}-2\sqrt{5-\sqrt{5}}}{8}\\[1em]\tan279°&=-\sqrt{5}-1-\sqrt{5+2\sqrt{5}}\end{align*}
$282°\ (=\frac{47}{30}\pi)$ $(=360°-78°)$
\begin{align*}\sin282°&=-\frac{\sqrt{30+6\sqrt{5}}+\sqrt{5}-1}{8}\\[1em]\cos282°&=\frac{\sqrt{10+2\sqrt{5}}+\sqrt{3}-\sqrt{15}}{8}\\[1em]\tan282°&=-\frac{\sqrt{10+2\sqrt{5}}+\sqrt{3}+\sqrt{15}}{2}\end{align*}
$285°\ (=\frac{19}{12}\pi)$ $(=360°-75°)$
\begin{align*}\sin285°&=-\frac{\sqrt{6}+\sqrt{2}}{4}\\[1em]\cos285°&=\frac{\sqrt{6}-\sqrt{2}}{4}\\[1em]\tan285°&=-2-\sqrt{3}\end{align*}
$288°\ (=\frac{8}{5}\pi)$ $(=360°-72°)$
\begin{align*}\sin288°&=-\frac{\sqrt{10+2\sqrt{5}}}{4}\\[1em]\cos288°&=\frac{\sqrt{5}-1}{4}\\[1em]\tan288°&=-\sqrt{5+2\sqrt{5}}\end{align*}
$291°\ (=\frac{97}{60}\pi)$ $(=360°-69°)$
\begin{align*}\sin291°&=-\frac{2\sqrt{20+2\sqrt{15}-10\sqrt{3}-4\sqrt{5}}+\sqrt{2}+\sqrt{6}+\sqrt{10}+\sqrt{30}}{16}\\[1em]\cos291°&=\frac{2\sqrt{20+10\sqrt{3}-4\sqrt{5}-2\sqrt{15}}+\sqrt{2}+\sqrt{10}-\sqrt{6}-\sqrt{30}}{16}\\[1em]\tan291°&=-\frac{\sqrt{110+28\sqrt{15}-60\sqrt{3}-46\sqrt{5}}+3\sqrt{3}+2\sqrt{5}-4-\sqrt{15}}{2}\end{align*}
$294°\ (=\frac{49}{30}\pi)$ $(=360°-66°)$
\begin{align*}\sin294°&=-\frac{\sqrt{5}+1+\sqrt{30-6\sqrt{5}}}{8}\\[1em]\cos294°&=\frac{\sqrt{3}+\sqrt{15}-\sqrt{10-2\sqrt{5}}}{8}\\[1em]\tan294°&=-\frac{\sqrt{10-2\sqrt{5}}+\sqrt{15}-\sqrt{3}}{2}\end{align*}
$297°\ (=\frac{33}{20}\pi)$ $(=360°-63°)$
\begin{align*}\sin297°&=-\frac{2\sqrt{5+\sqrt{5}}+\sqrt{10}-\sqrt{2}}{8}\\[1em]\cos297°&=\frac{2\sqrt{5+\sqrt{5}}+\sqrt{2}-\sqrt{10}}{8}\\[1em]\tan297°&=-\sqrt{5}+1-\sqrt{5-2\sqrt{5}}\end{align*}
$300°\ (=\frac{5}{3}\pi)$ $(=360°-60°)$
\begin{align*}\sin300°&=-\frac{\sqrt{3}}{2}\\[1em]\cos300°&=\frac{1}{2}\\[1em]\tan300°&=-\sqrt{3}\end{align*}
$303°\ (=\frac{101}{60}\pi)$ $(=360°-57°)$
\begin{align*}\sin303°&=-\frac{2\sqrt{20+10\sqrt{3}+4\sqrt{5}+2\sqrt{15}}+\sqrt{6}+\sqrt{10}-\sqrt{2}-\sqrt{30}}{16}\\[1em]\cos303°&=\frac{2\sqrt{20+4\sqrt{5}-10\sqrt{3}-2\sqrt{15}}+\sqrt{10}+\sqrt{30}-\sqrt{2}-\sqrt{6}}{16}\\[1em]\tan303°&=-\frac{\sqrt{110+60\sqrt{3}+46\sqrt{5}+28\sqrt{15}}-4-3\sqrt{3}-2\sqrt{5}-\sqrt{15}}{2}\end{align*}
$306°\ (=\frac{17}{10}\pi)$ $(=360°-54°)$
\begin{align*}\sin306°&=-\frac{\sqrt{5}+1}{4}\\[1em]\cos306°&=\frac{\sqrt{10-2\sqrt{5}}}{4}\\[1em]\tan306°&=-\frac{\sqrt{25+10\sqrt{5}}}{5}\end{align*}
$309°\ (=\frac{103}{60}\pi)$ $(=360°-51°)$
\begin{align*}\sin309°&=-\frac{2\sqrt{20+10\sqrt{3}-4\sqrt{5}-2\sqrt{15}}+\sqrt{6}+\sqrt{30}-\sqrt{2}-\sqrt{10}}{16}\\[1em]\cos309°&=\frac{\sqrt{2}+\sqrt{6}+\sqrt{10}+\sqrt{30}-2\sqrt{20+2\sqrt{15}-10\sqrt{3}-4\sqrt{5}}}{16}\\[1em]\tan309°&=-\frac{\sqrt{110+60\sqrt{3}-46\sqrt{5}-28\sqrt{15}}+4+3\sqrt{3}-2\sqrt{5}-\sqrt{15}}{2}\end{align*}
$312°\ (=\frac{26}{15}\pi)$ $(=360°-48°)$
\begin{align*}\sin312°&=-\frac{\sqrt{10+2\sqrt{5}}-\sqrt{3}+\sqrt{15}}{8}\\[1em]\cos312°&=\frac{\sqrt{30+6\sqrt{5}}+1-\sqrt{5}}{8}\\[1em]\tan312°&=-\frac{\sqrt{50-22\sqrt{5}}+3\sqrt{3}-\sqrt{15}}{2}\end{align*}
$315°\ (=\frac{7}{4}\pi)$ $(=360°-45°)$
\begin{align*}\sin315°&=-\frac{\sqrt{2}}{2}\\[1em]\cos315°&=\frac{\sqrt{2}}{2}\\[1em]\tan315°&=-1\end{align*}
$318°\ (=\frac{53}{30}\pi)$ $(=360°-42°)$
\begin{align*}\sin318°&=-\frac{\sqrt{30+6\sqrt{5}}+1-\sqrt{5}}{8}\\[1em]\cos318°&=\frac{\sqrt{10+2\sqrt{5}}+\sqrt{15}-\sqrt{3}}{8}\\[1em]\tan318°&=-\frac{\sqrt{3}+\sqrt{15}-\sqrt{10+2\sqrt{5}}}{2}\end{align*}
$321°\ (=\frac{107}{60}\pi)$ $(=360°-39°)$
\begin{align*}\sin321°&=-\frac{\sqrt{2}+\sqrt{6}+\sqrt{10}+\sqrt{30}-2\sqrt{20+2\sqrt{15}-10\sqrt{3}-4\sqrt{5}}}{16}\\[1em]\cos321°&=\frac{2\sqrt{20+10\sqrt{3}-4\sqrt{5}-2\sqrt{15}}+\sqrt{6}+\sqrt{30}-\sqrt{2}-\sqrt{10}}{16}\\[1em]\tan321°&=-\frac{\sqrt{110+28\sqrt{15}-60\sqrt{3}-46\sqrt{5}}+4+\sqrt{15}-3\sqrt{3}-2\sqrt{5}}{2}\end{align*}
$324°\ (=\frac{9}{5}\pi)$ $(=360°-36°)$
\begin{align*}\sin324°&=-\frac{\sqrt{10-2\sqrt{5}}}{4}\\[1em]\cos324°&=\frac{\sqrt{5}+1}{4}\\[1em]\tan324°&=-\sqrt{5-2\sqrt{5}}\end{align*}
$327°\ (=\frac{109}{60}\pi)$ $(=360°-33°)$
\begin{align*}\sin327°&=-\frac{2\sqrt{20+4\sqrt{5}-10\sqrt{3}-2\sqrt{15}}+\sqrt{10}+\sqrt{30}-\sqrt{2}-\sqrt{6}}{16}\\[1em]\cos327°&=\frac{2\sqrt{20+10\sqrt{3}+4\sqrt{5}+2\sqrt{15}}+\sqrt{6}+\sqrt{10}-\sqrt{2}-\sqrt{30}}{16}\\[1em]\tan327°&=-\frac{\sqrt{110+46\sqrt{5}-60\sqrt{3}-28\sqrt{15}}+3\sqrt{3}+\sqrt{15}-4-2\sqrt{5}}{2}\end{align*}
$330°\ (=\frac{11}{6}\pi)$ $(=360°-30°)$
\begin{align*}\sin330°&=-\frac{1}{2}\\[1em]\cos330°&=\frac{\sqrt{3}}{2}\\[1em]\tan330°&=-\frac{\sqrt{3}}{3}\end{align*}
$333°\ (=\frac{111}{60}\pi)$ $(=360°-27°)$
\begin{align*}\sin333°&=-\frac{2\sqrt{5+\sqrt{5}}+\sqrt{2}-\sqrt{10}}{8}\\[1em]\cos333°&=\frac{2\sqrt{5+\sqrt{5}}+\sqrt{10}-\sqrt{2}}{8}\\[1em]\tan333°&=-\sqrt{5}+1+\sqrt{5-2\sqrt{5}}\end{align*}
$336°\ (=\frac{28}{15}\pi)$ $(=360°-24°)$
\begin{align*}\sin336°&=-\frac{\sqrt{3}+\sqrt{15}-\sqrt{10-2\sqrt{5}}}{8}\\[1em]\cos336°&=\frac{\sqrt{5}+1+\sqrt{30-6\sqrt{5}}}{8}\\[1em]\tan336°&=-\frac{\sqrt{50+22\sqrt{5}}-3\sqrt{3}-\sqrt{15}}{2}\end{align*}
$339°\ (=\frac{113}{60}\pi)$ $(=360°-21°)$
\begin{align*}\sin339°&=-\frac{2\sqrt{20+10\sqrt{3}-4\sqrt{5}-2\sqrt{15}}+\sqrt{2}+\sqrt{10}-\sqrt{6}-\sqrt{30}}{16}\\[1em]\cos339°&=\frac{2\sqrt{20+2\sqrt{15}-10\sqrt{3}-4\sqrt{5}}+\sqrt{2}+\sqrt{6}+\sqrt{10}+\sqrt{30}}{16}\\[1em]\tan339°&=-\frac{\sqrt{110+60\sqrt{3}-46\sqrt{5}-28\sqrt{15}}+2\sqrt{5}+\sqrt{15}-4-3\sqrt{3}}{2}\end{align*}
$342°\ (=\frac{19}{10}\pi)$ $(=360°-18°)$
\begin{align*}\sin342°&=-\frac{\sqrt{5}-1}{4}\\[1em]\cos342°&=\frac{\sqrt{10+2\sqrt{5}}}{4}\\[1em]\tan342°&=-\frac{\sqrt{25-10\sqrt{5}}}{5}\end{align*}
$345°\ (=\frac{23}{12}\pi)$ $(=360°-15°)$
\begin{align*}\sin345°&=-\frac{\sqrt{6}-\sqrt{2}}{4}\\[1em]\cos345°&=\frac{\sqrt{6}+\sqrt{2}}{4}\\[1em]\tan345°&=-2+\sqrt{3}\end{align*}
$348°\ (=\frac{29}{15}\pi)$ $(=360°-12°)$
\begin{align*}\sin348°&=-\frac{\sqrt{10+2\sqrt{5}}+\sqrt{3}-\sqrt{15}}{8}\\[1em]\cos348°&=\frac{\sqrt{30+6\sqrt{5}}+\sqrt{5}-1}{8}\\[1em]\tan348°&=-\frac{3\sqrt{3}-\sqrt{15}-\sqrt{50-22\sqrt{5}}}{2}\end{align*}
$351°\ (=\frac{39}{20}\pi)$ $(=360°-9°)$
\begin{align*}\sin351°&=-\frac{\sqrt{2}+\sqrt{10}-2\sqrt{5-\sqrt{5}}}{8}\\[1em]\cos351°&=\frac{\sqrt{2}+\sqrt{10}+2\sqrt{5-\sqrt{5}}}{8}\\[1em]\tan351°&=-\sqrt{5}-1+\sqrt{5+2\sqrt{5}}\end{align*}
$354°\ (=\frac{59}{30}\pi)$ $(=360°-6°)$
\begin{align*}\sin354°&=-\frac{\sqrt{30-6\sqrt{5}}-\sqrt{5}-1}{8}\\[1em]\cos354°&=\frac{\sqrt{10-2\sqrt{5}}+\sqrt{3}+\sqrt{15}}{8}\\[1em]\tan354°&=-\frac{\sqrt{10-2\sqrt{5}}+\sqrt{3}-\sqrt{15}}{2}\end{align*}
$357°\ (=\frac{119}{60}\pi)$ $(=360°-3°)$
\begin{align*}\sin357°&=-\frac{\sqrt{30}+\sqrt{10}-\sqrt{6}-\sqrt{2}-2\sqrt{20-10\sqrt{3}+4\sqrt{5}-2\sqrt{15}}}{16}\\[1em]\cos357°&=\frac{2\sqrt{20+10\sqrt{3}+4\sqrt{5}+2\sqrt{15}}+\sqrt{2}+\sqrt{30}-\sqrt{6}-\sqrt{10}}{16}\\[1em]\tan357°&=-\frac{\sqrt{110+46\sqrt{5}-60\sqrt{3}-28\sqrt{15}}+4+2\sqrt{5}-3\sqrt{3}-\sqrt{15}}{2}\end{align*}
(2022/8)tan336°に誤りがありましたので修正しました。
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