Question

12 Encontre a primeira determinação positiva de cada um dos arcos a seguir e escreva a expressão geral dos arcos Côngruos ao arco indicado a) 800
b) 1 100°
c) 400°
d) 630°
e) 6 TT
F) 12TT/5
G) 5TT/2
H 17TY/3​

Answer 1

$\large\boxed{\begin{array}{l}\sf b)~\rm 1100^\circ|\underline{360^\circ}\\\rm\,\,\,-\underline{1080^\circ}~3\\\rm~~~~~~20^\circ\\\rm 1100^\circ=3\cdot360^\circ+20^\circ\\\rm \alpha=20^\circ+k\cdot 360^\circ,k\in\mathbb{Z}\end{array}}$

$\large\boxed{\begin{array}{l}\sf c)\\\rm400^\circ|\underline{360^\circ}\\\rm\!\!\!\!\!-\underline{ 360^\circ}~~1\\\rm~40^\circ\\\rm 400^\circ=1\cdot360^\circ+40^\circ\\\rm \alpha=40^\circ+k\cdot360^\circ,k\in\mathbb{Z}\end{array}}$

$\large\boxed{\begin{array}{l}\sf d)\\\rm\,630^\circ\,\,|\underline{360^\circ}\\\rm\!\!\!-\underline{360^\circ}~~1\\\rm\,270^\circ\\\rm 630^\circ=1\cdot360^\circ+270^\circ\\\rm \alpha=270^\circ+k\cdot 360^\circ,k\in\mathbb{Z}\end{array}}$

$\large\boxed{\begin{array}{l}\sf e)\\\rm 6\pi\,\,\,|\underline{2\pi}\\\rm\!\!\!\!-\underline{6\pi}~~\,3\\\rm\,\,0\\\rm 6\pi=3\cdot2\pi+0\\\rm \alpha=0+2k\pi,k\in\mathbb{Z}\end{array}}$

$\large\boxed{\begin{array}{l}\sf f)\\\rm\dfrac{12\pi}{5}=\dfrac{10\pi}{5}+\dfrac{2\pi}{5}\\\\\rm\dfrac{12\pi}{5}=2\pi+\dfrac{2\pi}{5}\\\\\rm \alpha=\dfrac{2\pi}{5}+2k\pi,k\in\mathbb{Z}\end{array}}$

$\large\boxed{\begin{array}{l}\sf g)\\\rm\dfrac{5\pi}{2}=\dfrac{4\pi}{2}+\dfrac{\pi}{2}\\\\\rm\dfrac{5\pi}{2}=2\pi+\dfrac{\pi}{2}\\\\\rm \alpha=\dfrac{\pi}{2}+2k\pi,k\in\mathbb{Z}\end{array}}$

$\large\boxed{\begin{array}{l}\sf h)\\\rm\dfrac{17\pi}{3}=\dfrac{12\pi}{3}+\dfrac{5\pi}{3}\\\\\rm\dfrac{17\pi}{3}=4\pi+\dfrac{5\pi}{3}\\\\\rm\dfrac{17\pi}{3}=2\cdot2\pi+\dfrac{5\pi}{3}\\\\\rm \alpha=\dfrac{5\pi}{3}+2k\pi,k\in\mathbb{Z}\end{array}}$