Instrucciones: Responde las siguientes preguntas.

• Utiliza la fórmula del coseno de la diferencia de dos ángulos para calcular a \(\cos 16^{\circ}\). Considera que \(\mbox{sen} 12^{\circ} \approx 0.2079\), \(\mbox{sen} 28^{\circ} \approx 0.4695\), \(\cos 12^{\circ} \approx 0.9781\) y \(\cos 28^{\circ} \approx 0.8829\).
  • \(\begin{array}{rcl} \cos \left ( 16^{\circ} \right ) & \approx & \left ( 0.9781 \right )\left ( 0.8829 \right ) - \left ( 0.2079 \right )\left ( 0.4695 \right ) \\ & \approx & 0.7660 \end{array}\)
  • \(\begin{array}{rcl} \cos \left ( 16^{\circ} \right ) & \approx & \left ( 0.2079 \right )\left ( 0.8829 \right ) - \left ( 0.4695 \right )\left ( 0.9781 \right ) \\ & \approx & -0.2757 \end{array}\)
  • \(\begin{array}{rcl} \cos \left ( 16^{\circ} \right ) & \approx & \left ( 0.2079 \right )\left ( 0.8829 \right ) + \left ( 0.4695 \right )\left ( 0.9781 \right ) \\ & \approx & 0.6428 \end{array}\)
  • \(\begin{array}{rcl} \cos \left ( 16^{\circ} \right ) & \approx & \left ( 0.9781 \right )\left ( 0.8829 \right ) + \left ( 0.2079 \right )\left ( 0.4695 \right ) \\ & \approx & 0.9612 \end{array}\)

• Identifica la identidad trigonométrica correcta.
  • \(\cos \left ( \alpha + \beta \right ) = \mbox{sen} \alpha \cos \beta + \mbox{sen} \beta \cos \alpha\)
  • \(\cos \left ( \alpha + \beta \right ) = \cos \alpha \cos \beta - \mbox{sen} \alpha \mbox{ sen} \beta\)
  • \(\cos \left ( \alpha + \beta \right ) = \cos \alpha \cos \beta + \mbox{sen} \alpha \mbox{ sen} \beta\)
  • \(\cos \left ( \alpha + \beta \right ) = \mbox{sen} \alpha \cos \beta - \mbox{sen} \beta \cos \alpha\)

• Identifica la identidad trigonométrica correcta
  • \(\cos \left ( \alpha - \beta \right ) = \cos \alpha \cos \beta + \mbox{sen} \alpha \mbox{sen} \beta\)
  • \(\cos \left ( \alpha - \beta \right ) = \mbox{sen} \alpha \cos \beta - \mbox{sen} \beta \cos \alpha\)
  • \(\cos \left ( \alpha - \beta \right ) = \mbox{sen} \alpha \cos \beta + \mbox{sen} \beta \cos \alpha\)
  • \(\cos \left ( \alpha - \beta \right ) = \cos \alpha \cos \beta - \mbox{sen} \alpha \mbox{sen} \beta\)

• Utiliza la fórmula del coseno de la suma de dos ángulos para calcular a \(\cos 53^{\circ}\). Considera que \(\mbox{sen} 21^{\circ} \approx 0.3584\), \(\mbox{sen} 32^{\circ} \approx 0.5299\), \(\cos 21^{\circ} \approx 0.9336\) y \(\cos 32^{\circ} \approx 0.8480\).
  • \(\begin{array}{rcl} \cos \left ( 53^{\circ} \right ) & \approx & \left ( 0.3584 \right )\left ( 0.8480 \right ) + \left ( 0.5299 \right )\left ( 0.9336 \right ) \\ & \approx & 0.7986 \end{array}\)
  • \(\begin{array}{rcl} \cos \left ( 53^{\circ} \right ) & \approx & \left ( 0.3584 \right )\left ( 0.8480 \right ) - \left ( 0.5299 \right )\left ( 0.9336 \right ) \\ & \approx & -0.1908 \end{array}\)
  • \(\begin{array}{rcl} \cos \left ( 53^{\circ} \right ) & \approx & \left ( 0.9336 \right )\left ( 0.8480 \right ) + \left ( 0.3584 \right )\left ( 0.5299 \right ) \\ & \approx & 0.9816 \end{array}\)
  • \(\begin{array}{rcl} \cos \left ( 53^{\circ} \right ) & \approx & \left ( 0.9336 \right )\left ( 0.8480 \right ) - \left ( 0.3584 \right )\left ( 0.5299 \right ) \\ & \approx & 0.6018 \end{array}\)

• Utiliza la fórmula del coseno de la suma de dos ángulos para calcular a \(\cos 71^{\circ}\). Considera que \(\mbox{sen} 17^{\circ} \approx 0.2924\), \(\mbox{sen} 54^{\circ} \approx 0.8090\), \(\cos 17^{\circ} \approx 0.9563\) y \(\cos 54^{\circ} \approx 0.5878\).
  • \(\begin{array}{rcl} \cos \left ( 71^{\circ} \right ) & \approx & \left ( 0.9563 \right )\left ( 0.5878 \right ) - \left ( 0.2924 \right )\left ( 0.8090 \right ) \\ & \approx & 0.3256 \end{array}\)
  • \(\begin{array}{rcl} \cos \left ( 71^{\circ} \right ) & \approx & \left ( 0.2924 \right )\left ( 0.5878 \right ) - \left ( 0.8090 \right )\left ( 0.9563 \right ) \\ & \approx & -0.6018 \end{array}\)
  • \(\begin{array}{rcl} \cos \left ( 71^{\circ} \right ) & \approx & \left ( 0.9563 \right )\left ( 0.5878 \right ) + \left ( 0.2924 \right )\left ( 0.8090 \right ) \\ & \approx & 0.7987 \end{array}\)
  • \(\begin{array}{rcl} \cos \left ( 71^{\circ} \right ) & \approx & \left ( 0.2924 \right )\left ( 0.5878 \right ) + \left ( 0.8090 \right )\left ( 0.9563 \right ) \\ & \approx & 0.9455 \end{array}\)