Question

Como resolver cos 195

Answer 1

Podemos reescrever o ângulo de $195^{\circ}$ como

$195^{\circ}=150^{\circ}+45^{\circ}$


E podemos aplicar a fómula do cosseno da soma de dois arcos:

$\cos(195^{\circ})=\cos(150^{\circ}+45^{\circ})\\ \\ \cos(195^{\circ})=\cos(150^{\circ})\cdot \cos(45^{\circ})-\mathrm{sen}(150^{\circ})\cdot \mathrm{sen}(45^{\circ})\\ \\ \cos(195^{\circ})=(-\frac{\sqrt{3}}{2})\cdot (\frac{\sqrt{2}}{2})-(\frac{1}{2})\cdot (\frac{\sqrt{2}}{2})\\ \\ \cos(195^{\circ})=\frac{-\sqrt{3}\cdot \sqrt{2}}{2\cdot 2}-\frac{1\cdot \sqrt{2}}{2\cdot 2}\\ \\ \boxed{ \begin{array}{c} \cos(195^{\circ})=\frac{-\sqrt{6}-\sqrt{2}}{4} \end{array} }$