Question

dados sen x = 4/5 (0<x<pi/2) e cos y =5/13 (0<y<pi/2), calcule.

a)sen (x+y)

b)cos (x+y)

c)sen (x-y)

d)cos (x-y)​

Answer 1

Resposta:

$\displaystyle y=\frac{\pi}{4}-x\\ \\ \sin y=\sin\left(\frac{\pi}{4}-x\right)\\ \\ \sin y=\sin\left(\frac{\pi}{4}\right)\cos x-\cos\left(\frac{\pi}{4}\right)\sin x\\ \\ \sin y=\frac{\sqrt{2}}{2}\cos x-\frac{\sqrt{2}}{2}\sin x\\ \\ \sin y=\frac{\sqrt{2}}{2}\left(\cos x-\sin x\right)\\ \\ \sin y=\frac{\sqrt{2}}{2}\left(\frac{12}{13}-\frac{5}{13}\right)\\ \\ \boxed{\sin y=\frac{7\sqrt{2}}{26}}$