Question

11.Obtenha as menores determinações não negativas dos arcos.
a) 1300°
b) 1440°
c) 170°
d) 11π/2 rad
e)43 π/5 rad
f) – 1200°

12.Dê as expressões gerais dos arcos côngruos a:
a) 1700°
b) – 700°
c)49 π/4 rad
d) 11π. rad
e)— 33 π/8 rad

Answer 1

$\boxed{\begin{array}{l}\rm 11)\\\tt a)~\sf 1300^\circ=3\cdot360+\boxed{\sf220^\circ}\\\tt b)~\sf1440^\circ=4\cdot360^\circ+\boxed{\sf 0^\circ}\\\tt c)~\sf 170^\circ\implies 1^a~determinac_{\!\!,}\tilde ao~n\tilde ao~negativa\\\tt d)~\sf\dfrac{11\pi}{2}=\dfrac{8\pi}{2}+\dfrac{3\pi}{2}=4\pi+\dfrac{3\pi}{2}\\\\\sf \dfrac{11\pi}{2}=2\cdot2\pi+\boxed{\sf\dfrac{3\pi}{2}~rad}\\\\\tt e)~\sf\dfrac{43\pi}{5}=\dfrac{40\pi}{5}+\dfrac{3\pi}{5}=4\cdot2\pi+\boxed{\sf\dfrac{3\pi}{5}~rad}\end{array}}$

$\boxed{\begin{array}{l}\tt f)~\sf -1200^\circ=-3\cdot360^\circ-120^\circ\\\sf 360^\circ-120^\circ=\boxed{\sf240^\circ}\end{array}}$

$\boxed{\begin{array}{l}\rm 12)\\\tt a)~\sf 1700^\circ=4\cdot360^\circ+260^\circ\\\sf \alpha^\circ=260^\circ+k\cdot 360^\circ,k\in\mathbb{Z}\\\tt b)~\sf -700^\circ=-1\cdot360^\circ-340^\circ\\\sf 360^\circ-340^\circ=20^\circ\\\sf \alpha^\circ=20^\circ+k\cdot 360^\circ,k\in\mathbb{Z}\\\tt c)~\sf\dfrac{49\pi}{4}~rad=\dfrac{48\pi}{4}+\dfrac{\pi}{4}=6\cdot2\pi+\dfrac{\pi}{4}\\\\\sf\alpha=\dfrac{\pi}{4}+2k\pi,k\in\mathbb{Z}\\\tt d)~\sf 11\pi~rad=5\cdot2\pi+\pi\\\sf \alpha=\pi+2k\pi,k\in\mathbb{Z}\end{array}}$

$\boxed{\begin{array}{l}\tt e)~\sf-\dfrac{33\pi}{8}~rad=-\dfrac{32\pi}{8}-\dfrac{\pi}{8}=-2\cdot2\pi-\dfrac{\pi}{8}\\\sf 2\pi-\dfrac{\pi}{8}=\dfrac{15\pi}{8}\\\\\sf \alpha=\dfrac{15\pi}{8}+2k\pi,k\in\mathbb{Z}\end{array}}$