Instrucciones: Responde las siguientes preguntas.

• Identifica la identidad trigonométrica correcta.
  • $\text{sen}(\alpha +\beta )=\text{sen}\alpha \cos \beta +\text{sen}\beta \cos \alpha$
  • $\text{sen}(\alpha +\beta )=\text{sen}\alpha \cos \alpha -\text{sen}\beta \cos \beta$
  • $\text{sen}(\alpha +\beta )=\text{sen}\alpha \cos \alpha +\text{sen}\beta \cos \beta$
  • $\text{sen}(\alpha +\beta )=\text{sen}\alpha \cos \beta -\text{sen}\beta \cos \alpha$

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

• Identifica la identidad trigonométrica correcta.
  • $\text{sen}(\alpha -\beta )=\text{sen}\alpha \cos \alpha +\text{sen}\beta \cos \beta$
  • $\text{sen}(\alpha -\beta )=\text{sen}\alpha \cos \beta +\text{sen}\beta \cos \alpha$
  • $\text{sen}(\alpha -\beta )=\text{sen}\alpha \cos \alpha -\text{sen}\beta \cos \beta$
  • $\text{sen}(\alpha -\beta )=\text{sen}\alpha \cos \beta -\text{sen}\beta \cos \alpha$

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

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