Question

calcule o seno de 165 usando as formulas de adição ou subtração

Answer 1

sen(165°) = sen(120° + 45°)

= sen 120° · cos 45° + sen 45° · cos 120°

Como

$sen\: 120\° = sen\: 60\º = \frac{ \sqrt{3}}{2}\\ cos\: 120\° = -cos\: 60\º = -\frac{1}{2}$

Então


$\frac{ \sqrt{3} }{2} \cdot \frac{ \sqrt{2} }{2} + \frac{ \sqrt{2} }{2} \cdot (- \frac{ 1 }{2} )\\\\ = \frac{\sqrt{3}}{2}\cdot \frac{\sqrt{2}}{2}-\frac{\sqrt{2}}{2}\cdot \frac{1}{2}\\\\ = \frac{\sqrt{3}}{2\sqrt{2}}-\frac{1}{2\sqrt{2}}\\\\ = \frac{\sqrt{3}-1}{2\sqrt{2}} = \frac{\left(\sqrt{3}-1\right)\sqrt{2}}{2\sqrt{2}\sqrt{2}}\\\\ = \frac{\sqrt{2}\left(\sqrt{3}-1\right)}{4} \;\;ou\;\;0.25882$