Question

Obtenha a determinação principal e indique o quadrante ou o ponto.
a) 43π/6 b) 1750° c)-21π/5 d)-3π

Answer 1

$\boxed{\begin{array}{l}\tt a)~\sf\dfrac{43\pi}{6}=\dfrac{36\pi}{6}+\dfrac{7\pi}{6}=6\pi+\dfrac{7\pi}{6}\\\sf\dfrac{43\pi}{6}=3\cdot2\pi+\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\underbrace{\sf\dfrac{7\pi}{6}}_{determinac_{\!\!,}\tilde ao~principal}\!\!\!\!\!\!\!\!\!\to \in 3^o~quadrante\\\tt b)~\sf 1750^\circ=4\cdot360^\circ+\!\!\!\!\!\!\!\!\!\underbrace{\sf310^\circ}_{ determinac_{\!\!,}\tilde ao~principal}\to \in 4^o~quadrante\end{array}}$

$\boxed{\begin{array}{l}\tt c)~\sf-\dfrac{21\pi}{5}=-\dfrac{20\pi}{5}-\dfrac{\pi}{5}=-4\pi-\dfrac{\pi}{5}\\\sf-\dfrac{21\pi}{5}=-2\cdot2\pi-\dfrac{\pi}{5}\\\sf 2\pi-\dfrac{\pi}{5}=\!\!\!\!\!\!\!\!\!\!\!\underbrace{\sf\dfrac{11\pi}{5}}_{determinac_{\!\!,}\tilde ao~principal}\!\!\!\!\!\1\!\to\in 4^o~quadrante\\\tt d)~\sf -3\pi=-1\cdot2\pi-\pi\\\sf 2\pi-\pi=\!\!\!\!\!\!\!\!\!\!\!\!\!\underbrace{\pi}_{ determinac_{\!\!,}\tilde ao~principal}\!\!\!\!\!\!\!\to ponto(\pi,0)\end{array}}$