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Valores de las funciones Seno y Coseno
para los ángulos múltiplos de 3

$\left\{\vphantom{\begin{array}{lcl} sen 33^o & =&\displaystyle{\sqrt{8+\sqrt{... ...}}}-\sqrt{8-\sqrt{15}-\sqrt{3}-\sqrt{10-2\sqrt{5}}}\over8} \end{array}}\right.$ $\begin{array}{lcl} sen 33^o & =&\displaystyle{\sqrt{8+\sqrt{3}+\sqrt{15}+\sqr... ...2\sqrt{5}}}-\sqrt{8-\sqrt{15}-\sqrt{3}-\sqrt{10-2\sqrt{5}}}\over8} \end{array}$

$\left\{\vphantom{\begin{array}{lclcl} sen 36^o & =& \displaystyle{\sqrt{10-2\... ...{6+2\sqrt{5}}\over 4}& = &\displaystyle{\sqrt{5}+1\over 4} \end{array}}\right.$ $\begin{array}{lclcl} sen 36^o & =& \displaystyle{\sqrt{10-2\sqrt{5}}\over 4}&... ...le{\sqrt{6+2\sqrt{5}}\over 4}& = &\displaystyle{\sqrt{5}+1\over 4} \end{array}$

$\left\{\vphantom{\begin{array}{lcl} sen 39^o &=&\displaystyle{\sqrt{2}\over16... ...2\sqrt{5}-\sqrt{15}}+\sqrt{15}-\sqrt{5}+\sqrt{3}-1\right]} \end{array}}\right.$ $\begin{array}{lcl} sen 39^o &=&\displaystyle{\sqrt{2}\over16}\displaystyle{\l... ...sqrt{3}-2\sqrt{5}-\sqrt{15}}+\sqrt{15}-\sqrt{5}+\sqrt{3}-1\right]} \end{array}$

$\left\{\vphantom{\begin{array}{lcl} sen 42^o & =& \displaystyle{1-\sqrt{5}+\s... ...isplaystyle{\sqrt{15}-\sqrt{3}+\sqrt{10+2\sqrt{5}}\over 8} \end{array}}\right.$ $\begin{array}{lcl} sen 42^o & =& \displaystyle{1-\sqrt{5}+\sqrt{30+6\sqrt{5}}... ... & =& \displaystyle{\sqrt{15}-\sqrt{3}+\sqrt{10+2\sqrt{5}}\over 8} \end{array}$

$\left\{\vphantom{\begin{array}{lcl} sen 45^o & =& \displaystyle{\sqrt{2}\over... ...\ & & \\ cos 45^o & =& \displaystyle{\sqrt{2}\over2} \end{array}}\right.$ $\begin{array}{lcl} sen 45^o & =& \displaystyle{\sqrt{2}\over 2} \\ & & \\ cos 45^o & =& \displaystyle{\sqrt{2}\over2} \end{array}$