Question

Qual é o valor de sen 105º ???

Answer 1

$sen \;105\° = sen (45\° + 60\°)\\\\ = sen\;60\° \cdot cos\;45\° + cos\;60\° \cdot sen\;45\°\\\\ = \frac{ \sqrt{3} }{2} \cdot \frac{ \sqrt{2} }{2} + \frac{1 }{2} \cdot \frac{ \sqrt{2} }{2} \\\\ = \frac{ \sqrt{6} }{2}+\frac{ \sqrt{2} }{4}\\\\ = \frac{ \sqrt{6} + \sqrt{2} }{4}$

$\framebox[1.1\width]{\quad sen 105\° = \frac{\sqrt{6} + \sqrt{2} }{4} }$