Instrucciones: Responde las siguientes preguntas.

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

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

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

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

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