Question

Qual é o valor da expressão sen (π/2)-cos(π)-sen(3π/2)? *
-1
1
2
3
Nenhuma dessas alternativas é correta

Answer 1

$\displaystyle \text{sen}(\frac{\pi}{2})-\text{cos}(\pi)-\text{sen}(\frac{3\pi}{2}) \\\\ \underline{\text{sabemos que}}: \\\\ \frac{\pi}{2}=90^\circ\to \text{sen}(90^\circ)=1 \\\\ \pi = 180^\circ \to \text{cos} (180^\circ)=-1 \\\\ \frac{3\pi}{2} = 270^{\circ} \to \text{sen(270}^\circ)=-1 \\\\ \underline{\text{Substituindo}}: \\\\ \text{sen}(\frac{\pi}{2})-\text{cos}(\pi)-\text{sen}(\frac{3\pi}{2}) = 1-(-1)-(-1) \\\\ \text{sen}(\frac{\pi}{2})-\text{cos}(\pi)-\text{sen}(\frac{3\pi}{2})= 3$

Portanto :

$\displaystyle \text{sen}(\frac{\pi}{2})-\text{cos}(\pi)-\text{sen}(\frac{3\pi}{2}) = \huge\boxed{3}\checkmark$