Instrucciones: Responde las siguientes preguntas.

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

• Utiliza la fórmula del seno de la diferencia de dos ángulos para calcular a \(\mbox{sen} 18^{\circ}\). Considera que \(\mbox{sen} 4^{\circ} \approx 0.0698\), \(\mbox{sen} 22^{\circ} \approx 0.3746\), \(\cos 4^{\circ} \approx 0.9976\) y \(\cos 22^{\circ} \approx 0.9272\).
  • \(\begin{array}{rcl} \mbox{sen} \left ( 18^{\circ} \right ) & \approx & \left ( 0.3746 \right )\left ( 0.9976 \right ) - \left ( 0.0698 \right )\left ( 0.9272 \right ) \\ & \approx & 0.3090 \end{array}\)
  • \(\begin{array}{rcl} \mbox{sen} \left ( 18^{\circ} \right ) & \approx & \left ( 0.0698 \right )\left ( 0.9272 \right ) + \left ( 0.3746 \right )\left ( 0.9976 \right ) \\ & \approx & 0.4384 \end{array}\)
  • \(\begin{array}{rcl} \mbox{sen} \left ( 18^{\circ} \right ) & \approx & \left ( 0.0698 \right )\left ( 0.9976 \right ) - \left ( 0.3746 \right )\left ( 0.9272 \right ) \\ & \approx & -0.2777 \end{array}\)
  • \(\begin{array}{rcl} \mbox{sen} \left ( 18^{\circ} \right ) & \approx & \left ( 0.0698 \right )\left ( 0.9976 \right ) + \left ( 0.3746 \right )\left ( 0.9272 \right ) \\ & \approx & 0.4170 \end{array}\)

• Utiliza la fórmula del seno de la suma de dos ángulos para calcular a \(\mbox{sen} 72^{\circ}\). Considera que \(\mbox{sen} 28^{\circ} \approx 0.4695\), \(\mbox{sen} 44^{\circ} \approx 0.6947\), \(\cos 28^{\circ} \approx 0.8829\) y \(\cos 44^{\circ} \approx 0.7193\).
  • \(\begin{array}{rcl} \mbox{sen} \left ( 72^{\circ} \right ) & \approx & \left ( 0.4695 \right )\left ( 0.8829 \right ) - \left ( 0.6947 \right )\left ( 0.7193 \right ) \\ & \approx & -0.0852 \end{array}\)
  • \(\begin{array}{rcl} \mbox{sen} \left ( 72^{\circ} \right ) & \approx & \left ( 0.4695 \right )\left ( 0.8829 \right ) + \left ( 0.6947 \right )\left ( 0.7193 \right ) \\ & \approx & 0.9142 \end{array}\)
  • \(\begin{array}{rcl} \mbox{sen} \left ( 72^{\circ} \right ) & \approx & \left ( 0.4695 \right )\left ( 0.7193 \right ) + \left ( 0.6947 \right )\left ( 0.8829 \right ) \\ & \approx & 0.9511 \end{array}\)
  • \(\begin{array}{rcl} \mbox{sen} \left ( 72^{\circ} \right ) & \approx & \left ( 0.4695 \right )\left ( 0.7193 \right ) - \left ( 0.6947 \right )\left ( 0.8829 \right ) \\ & \approx & -0.2756 \end{array}\)

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

• Utiliza la fórmula del seno de la suma de dos ángulos para calcular a \(\mbox{sen} 56^{\circ}\). Considera que \(\mbox{sen} 14^{\circ} \approx 0.2419\), \(\mbox{sen} 42^{\circ} \approx 0.6691\), \(\cos 14^{\circ} \approx 0.9703\) y \(\cos 42^{\circ} \approx 0.7431\).
  • \(\begin{array}{rcl} \mbox{sen} \left ( 56^{\circ} \right ) & \approx & \left ( 0.2419 \right )\left ( 0.7431 \right ) - \left ( 0.6691 \right )\left ( 0.9703 \right ) \\ & \approx & -0.4695 \end{array}\)
  • \(\begin{array}{rcl} \mbox{sen} \left ( 56^{\circ} \right ) & \approx & \left ( 0.2419 \right )\left ( 0.9703 \right ) - \left ( 0.6691 \right )\left ( 0.7431 \right ) \\ & \approx & -0.2625 \end{array}\)
  • \(\begin{array}{rcl} \mbox{sen} \left ( 56^{\circ} \right ) & \approx & \left ( 0.2419 \right )\left ( 0.7431 \right ) + \left ( 0.6691 \right )\left ( 0.9703 \right ) \\ & \approx & 0.8290 \end{array}\)
  • \(\begin{array}{rcl} \mbox{sen} \left ( 56^{\circ} \right ) & \approx & \left ( 0.2419 \right )\left ( 0.9703 \right ) + \left ( 0.6691 \right )\left ( 0.7431 \right ) \\ & \approx & 0.7319 \end{array}\)