Instrucciones: Responde las siguientes preguntas.

• Calcula los valores de las otras razones trigonométricas para el ángulo $\alpha$, si se sabe que $\sin \alpha ={\displaystyle \frac{1}{8}}$.
  • $\begin{array}{rcl}\cos \alpha & =& {\displaystyle \frac{\sqrt{59}}{8}}\\ \\ \tan \alpha & =& {\displaystyle \frac{\sqrt{59}}{59}}\\ \\ \cot \alpha & =& \sqrt{59}\\ \\ \sec \alpha & =& {\displaystyle \frac{8\sqrt{59}}{59}}\\ \\ \csc \alpha & =& 8\end{array}$
  • $\begin{array}{rcl}\cos \alpha & =& {\displaystyle \frac{\sqrt{55}}{8}}\\ \\ \tan \alpha & =& {\displaystyle \frac{\sqrt{55}}{55}}\\ \\ \cot \alpha & =& \sqrt{55}\\ \\ \sec \alpha & =& {\displaystyle \frac{8\sqrt{55}}{55}}\\ \\ \csc \alpha & =& 8\end{array}$
  • $\begin{array}{rcl}\cos \alpha & =& {\displaystyle \frac{3\sqrt{7}}{8}}\\ \\ \tan \alpha & =& {\displaystyle \frac{\sqrt{7}}{21}}\\ \\ \cot \alpha & =& 3\sqrt{7}\\ \\ \sec \alpha & =& {\displaystyle \frac{8\sqrt{7}}{21}}\\ \\ \csc \alpha & =& 8\end{array}$
  • $\begin{array}{rcl}\cos \alpha & =& {\displaystyle \frac{3\sqrt{6}}{8}}\\ \\ \tan \alpha & =& {\displaystyle \frac{\sqrt{6}}{18}}\\ \\ \cot \alpha & =& 3\sqrt{6}\\ \\ \sec \alpha & =& {\displaystyle \frac{4\sqrt{6}}{9}}\\ \\ \csc \alpha & =& 8\end{array}$

• Calcula los valores de las otras razones trigonométricas para el ángulo $\alpha$, si se sabe que $\cos \alpha ={\displaystyle \frac{4}{5}}$.
  • $\begin{array}{rcl}\sin \alpha & =& {\displaystyle \frac{\sqrt{2}}{5}}\\ \\ \tan \alpha & =& {\displaystyle \frac{\sqrt{2}}{4}}\\ \\ \cot \alpha & =& 2\sqrt{2}\\ \\ \sec \alpha & =& {\displaystyle \frac{5}{4}}\\ \\ \csc \alpha & =& {\displaystyle \frac{5\sqrt{2}}{2}}\end{array}$
  • $\begin{array}{rcl}\sin \alpha & =& {\displaystyle \frac{3}{5}}\\ \\ \tan \alpha & =& {\displaystyle \frac{3}{4}}\\ \\ \cot \alpha & =& {\displaystyle \frac{4}{3}}\\ \\ \sec \alpha & =& {\displaystyle \frac{5}{4}}\\ \\ \csc \alpha & =& {\displaystyle \frac{5}{3}}\end{array}$
  • $\begin{array}{rcl}\sin \alpha & =& {\displaystyle \frac{2}{5}}\\ \\ \tan \alpha & =& {\displaystyle \frac{1}{2}}\\ \\ \cot \alpha & =& 2\\ \\ \sec \alpha & =& {\displaystyle \frac{5}{4}}\\ \\ \csc \alpha & =& {\displaystyle \frac{5}{2}}\end{array}$
  • $\begin{array}{rcl}\sin \alpha & =& {\displaystyle \frac{1}{5}}\\ \\ \tan \alpha & =& {\displaystyle \frac{1}{4}}\\ \\ \cot \alpha & =& 4\\ \\ \sec \alpha & =& {\displaystyle \frac{5}{4}}\\ \\ \csc \alpha & =& 5\end{array}$

• Calcula los valores de las otras razones trigonométricas para el ángulo $\alpha$, si se sabe que $\cos \alpha ={\displaystyle \frac{2}{11}}$.
  • $\begin{array}{rcl}\sin \alpha & =& {\displaystyle \frac{3\sqrt{13}}{11}}\\ \\ \tan \alpha & =& {\displaystyle \frac{3\sqrt{13}}{2}}\\ \\ \cot \alpha & =& {\displaystyle \frac{2\sqrt{13}}{39}}\\ \\ \sec \alpha & =& {\displaystyle \frac{11}{2}}\\ \\ \csc \alpha & =& {\displaystyle \frac{11\sqrt{13}}{39}}\end{array}$
  • $\begin{array}{rcl}\sin \alpha & =& {\displaystyle \frac{\sqrt{102}}{11}}\\ \\ \tan \alpha & =& {\displaystyle \frac{\sqrt{102}}{2}}\\ \\ \cot \alpha & =& {\displaystyle \frac{\sqrt{102}}{51}}\\ \\ \sec \alpha & =& {\displaystyle \frac{11}{2}}\\ \\ \csc \alpha & =& {\displaystyle \frac{11\sqrt{102}}{102}}\end{array}$
  • $\begin{array}{rcl}\sin \alpha & =& {\displaystyle \frac{\sqrt{111}}{11}}\\ \\ \tan \alpha & =& {\displaystyle \frac{\sqrt{111}}{2}}\\ \\ \cot \alpha & =& {\displaystyle \frac{2\sqrt{111}}{111}}\\ \\ \sec \alpha & =& {\displaystyle \frac{11}{2}}\\ \\ \csc \alpha & =& {\displaystyle \frac{11\sqrt{111}}{111}}\end{array}$
  • $\begin{array}{rcl}\sin \alpha & =& {\displaystyle \frac{4\sqrt{7}}{11}}\\ \\ \tan \alpha & =& 2\sqrt{7}\\ \\ \cot \alpha & =& {\displaystyle \frac{\sqrt{7}}{14}}\\ \\ \sec \alpha & =& {\displaystyle \frac{11}{2}}\\ \\ \csc \alpha & =& {\displaystyle \frac{11\sqrt{7}}{28}}\end{array}$

• Calcula los valores de las otras razones trigonométricas para el ángulo $\alpha$, si se sabe que $\tan \alpha ={\displaystyle \frac{13}{8}}$.
  • $\begin{array}{rcl}\sin \alpha & =& {\displaystyle \frac{13\sqrt{226}}{226}}\\ \\ \cos \alpha & =& {\displaystyle \frac{4\sqrt{226}}{113}}\\ \\ \cot \alpha & =& {\displaystyle \frac{8}{13}}\\ \\ \sec \alpha & =& {\displaystyle \frac{\sqrt{226}}{8}}\\ \\ \csc \alpha & =& {\displaystyle \frac{\sqrt{226}}{13}}\end{array}$
  • $\begin{array}{rcl}\sin \alpha & =& {\displaystyle \frac{13\sqrt{246}}{246}}\\ \\ \cos \alpha & =& {\displaystyle \frac{4\sqrt{246}}{123}}\\ \\ \cot \alpha & =& {\displaystyle \frac{8}{13}}\\ \\ \sec \alpha & =& {\displaystyle \frac{\sqrt{246}}{8}}\\ \\ \csc \alpha & =& {\displaystyle \frac{\sqrt{246}}{13}}\end{array}$
  • $\begin{array}{rcl}\sin \alpha & =& {\displaystyle \frac{13\sqrt{233}}{233}}\\ \\ \cos \alpha & =& {\displaystyle \frac{8\sqrt{233}}{233}}\\ \\ \cot \alpha & =& {\displaystyle \frac{8}{13}}\\ \\ \sec \alpha & =& {\displaystyle \frac{\sqrt{233}}{8}}\\ \\ \csc \alpha & =& {\displaystyle \frac{\sqrt{233}}{13}}\end{array}$
  • $\begin{array}{rcl}\sin \alpha & =& {\displaystyle \frac{13\sqrt{201}}{201}}\\ \\ \cos \alpha & =& {\displaystyle \frac{8\sqrt{201}}{201}}\\ \\ \cot \alpha & =& {\displaystyle \frac{8}{13}}\\ \\ \sec \alpha & =& {\displaystyle \frac{\sqrt{201}}{8}}\\ \\ \csc \alpha & =& {\displaystyle \frac{\sqrt{201}}{13}}\end{array}$

• Calcula los valores de las otras razones trigonométricas para el ángulo $\alpha$, si se sabe que $\sin \alpha ={\displaystyle \frac{2}{5}}$.
  • $\begin{array}{rcl}\cos \alpha & =& {\displaystyle \frac{\sqrt{21}}{5}}\\ \\ \tan \alpha & =& {\displaystyle \frac{2\sqrt{21}}{21}}\\ \\ \cot \alpha & =& {\displaystyle \frac{\sqrt{21}}{2}}\\ \\ \sec \alpha & =& {\displaystyle \frac{5\sqrt{21}}{21}}\\ \\ \csc \alpha & =& {\displaystyle \frac{5}{2}}\end{array}$
  • $\begin{array}{rcl}\cos \alpha & =& {\displaystyle \frac{\sqrt{22}}{5}}\\ \\ \tan \alpha & =& {\displaystyle \frac{\sqrt{22}}{11}}\\ \\ \cot \alpha & =& {\displaystyle \frac{\sqrt{22}}{2}}\\ \\ \sec \alpha & =& {\displaystyle \frac{5\sqrt{22}}{22}}\\ \\ \csc \alpha & =& {\displaystyle \frac{5}{2}}\end{array}$
  • $\begin{array}{rcl}\cos \alpha & =& {\displaystyle \frac{\sqrt{17}}{5}}\\ \\ \tan \alpha & =& {\displaystyle \frac{2\sqrt{17}}{17}}\\ \\ \cot \alpha & =& {\displaystyle \frac{\sqrt{17}}{2}}\\ \\ \sec \alpha & =& {\displaystyle \frac{5\sqrt{17}}{17}}\\ \\ \csc \alpha & =& {\displaystyle \frac{5}{2}}\end{array}$
  • $\begin{array}{rcl}\cos \alpha & =& {\displaystyle \frac{4}{5}}\\ \\ \tan \alpha & =& 2\\ \\ \cot \alpha & =& {\displaystyle \frac{1}{2}}\\ \\ \sec \alpha & =& {\displaystyle \frac{5}{4}}\\ \\ \csc \alpha & =& {\displaystyle \frac{5}{2}}\end{array}$