Question

Dê as expressões gerais dos arcos côngruos a:
a) 1600
b) - 600
c)49pi/4 rad

Answer 1

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$\tt a)~\sf 1600^\circ=160^\circ+4\cdot 360^\circ\\\huge\boxed{\boxed{\boxed{\boxed{\sf\alpha=160^\circ+k\cdot360^\circ,k\in\mathbb{Z}}}}}$

$\tt b)~\sf -600^\circ=-240^\circ-1\cdot360^\circ\\\sf360-240^\circ=120^\circ\\\huge\boxed{\boxed{\boxed{\boxed{\sf \alpha=120^\circ+k\cdot 360^\circ,k\in\mathbb{Z}}}}}$

$\tt c)~\sf \dfrac{49\pi}{4}=\dfrac{48\pi}{4}+\dfrac{\pi}{4}=12\pi+\dfrac{\pi}{4}\\\sf \dfrac{49\pi}{4}=\dfrac{\pi}{4}+6\cdot2\pi\\\huge\boxed{\boxed{\boxed{\boxed{\sf\alpha=\dfrac{\pi}{4}+2k\pi,k\in\mathbb{Z}}}}}$