Question

usando a formula da adição , determine sen 165 , sen 225 , cos 225

Answer 1

Note que Sen120°=Sen60° = $\frac{ \sqrt{3} }{2}$
Então:
Sen165°=Sen(120° + 45°)
Assim temos:
Sen(120° + 45°) = Sen120°Cos45° + Sen45°Cos120°
$\frac{\sqrt{3} }{2}.\frac{\sqrt{2} }{2}+\frac{\sqrt{2} }{2} .(-\frac{1}{2})=$
$\frac{ \sqrt{6} }{4} - \frac{ \sqrt{2} }{4}$
$\frac{ \sqrt{6}- \sqrt{2} }{4}$

Sen225°=Sen(180° + 45°)
Sen180°Cos45° + Sen45°Cos180°
$0. \frac{ \sqrt{2} }{2} + \frac{ \sqrt{2} }{2}.(-1)$
$- \frac{ \sqrt{2} }{2}$

Cos225°=Cos(180° + 45°)
Cos(180° + 45°) = Cos180°Cos45° - Sen180°Sen45°
$-1. \frac{ \sqrt{2} }{2} -0. \frac{ \sqrt{2} }{2}$
$- \frac{ \sqrt{2} }{2}$