Question

Ache o valor da expressao:
15π
2

sen 8TT+cos 11π -sen

Answer 1

• Vamos a Expressão

$\\\\\\\sf \displaystyle sen8\pi +cos11\pi -sen\frac{15\pi }{2}\\\\\\\sf sin \left(\frac{15\pi }{2}\right)=cos \left(\frac{\pi }{2}-\frac{15\pi }{2}\right)\\\\\\\sf =sin \left(8\pi \right)+\cos \left(11\pi \right)-cos \left(\frac{\pi }{2}-\frac{15\pi }{2}\right)\\\\\\\sf =sin \left(8\pi \right)+cos \left(11\pi \right)-cos \left(-7\pi \right)\\\\\\\sf =sin \left(8\pi \right)+cos \left(11\pi \right)-cos \left(7\pi \right)$

$\sf \sf =sin \left(0\right)+cos \left(11\pi \right)-cos \left(7\pi \right)\\\\\\\sf =sin \left(0\right)+cos \left(\pi \right)-cos \left(7\pi \right)\\\\\\\sf =sin \left(0\right)+cos \left(\pi \right)-cos \left(\pi \right)\\\\\\=sin \left(0\right)$

• Use a identidade trivial de sen(0) =0

$\boxed{\sf S=\{ 0\}}$