Question

Se ∝ é um ângulo, tal que 0 ∠ ∝ ∠ $\frac{\pi }{2}$, e se ∝ = a, então a tg (π - a) é igual a:

Answer 1

Resposta:

$\pi -a=-a$

$tg(\pi -a)=tg(-a)$

Logo é negativa.

Answer 2

$\tan(\pi-\alpha)=\\\\\\\dfrac{\sin(\pi-\alpha)}{\cos(\pi-\alpha)}=\\\\\\\dfrac{\sin(\pi)\cos(\alpha)-\cos(\pi)\sin(\alpha)}{\cos(\pi)\cos(\alpha)+\sin(\pi)\sin(\alpha)}=\\\\\\\dfrac{0\cdot\cos(\alpha)-(-1)\sin(\alpha)}{(-1)\cos(\alpha)+0\cdot\sin(\alpha)}=\\\\\\\dfrac{\sin(\alpha)}{-\cos(\alpha)}=\\\\\\\boxed{-\tan(\alpha)}$