Instrucciones: Responde las siguientes preguntas.

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

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

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

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

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