Question

Qual a primeira determinação positiva de um arco de 4536° ?

a) 12 . 2π + π
b) 12 . 2π + 2π/3
c) 12 . 2π + π/3
d) 12 . 2π + 6π/5
e) 12 . 2π + π/5​

Answer 1

$\boxed{\begin{array}{l}\rm 4536^\circ=12\cdot360^\circ+216^\circ\\\rm 216^\circ=\dfrac{216\div36}{180\div36}\pi~rad\\\\\rm 216^\circ=\dfrac{6\pi}{5}~rad\\\\\rm\alpha=\dfrac{6\pi}{5}+2k\pi,k\in\mathbb{Z}\\\huge\boxed{\boxed{\boxed{\boxed{\rm\dagger~\red{\maltese}~\blue{alternativa~d}}}}}\end{array}}$