Question

Calcule o valor de sen(a+b) para a=π/4 e b=π/3
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Answer 1

$\sin( \alpha + \beta ) = \sin( \alpha ) . \cos( \beta ) + \sin( \beta ) . \cos( \alpha ) \\ \\ \\ \sin( \frac{\pi}{4} + \frac{\pi}{3} ) = \sin(45) . \cos(60) + \sin(60) . \cos(45) \\ \\ = \frac{ \sqrt{2} }{2} . \frac{1}{2} + \frac{ \sqrt{3} }{2} . \frac{ \sqrt{2} }{2} = \frac{ \sqrt{2} }{4} + \frac{ \sqrt{6} }{4} \\ \\ = \frac{ \sqrt{2} + \sqrt{6} }{4}$