Question

PUC: calcular E=sen(-x)+sen(pi+x) - sen(pi/2 - x)? a resposta e -2*sen x , preciso da resolução!

Answer 1

sen(-x)=-senx

 

sen(a+b)=sena.cosb+senb.cosa

sen(pi+x)=senpi.cosx+senx.cospi

sen(pi+x)=-senx

 

sen(a-b)=sena.cosb-senb.cosa

sen(pi/2-x)=senpi/2.cosx-senx.cospi/2

sen(pi/2)=cosx

 

E=-senx-ssenx-cosx

E=-2senx-cosx

Answer 2

Só para confirmar!

 

$\begin{cases} \sin (x + y) = \sin x \cdot \cos y + \sin y \cdot \cos x \\ \sin (x - y) = \sin x \cdot \cos y - \sin y \cdot \cos x\end{cases}$

 

$E = \sin (- x) + \sin (\pi + x) - \sin \left ( \frac{\pi }{2} - x \right )$

 

$E = \sin (0 - x) + \sin (\pi + x) - \sin \left ( \frac{\pi }{2} - x \right )$

 

$E = (\sin 0 \cdot \cos x - \sin x \cdot \cos 0) + (\sin \pi \cdot \cos x + \sin x \cdot \cos \pi) - \left [ \sin \left ( \frac{\pi}{2} \right ) \cdot \cos x - \sin x \cdot \cos \left ( \frac{\pi }{2} \right ) \right ]$

 

$E = 0 \cdot \cos x - \sin x \cdot 1 + 0 \cdot \cos x + \sin x \cdot - 1 - (1 \cdot \cos x - \sin x \cdot 0)$

 

$E = 0 - \sin x + 0 - \sin x - \cos x + 0$

 

$\boxed{E = - 2 \cdot \sin x - \cos x}$