Question

Qual o valor de 3π/5 rad em graus e 240° em rad, respectivamente? *
108 graus ; 4π/3 rad
216 graus ; 8π/3 rad
108 graus ; 2π/3 rad
216 graus ; 4π/3 rad
108 graus ; π/3 rad

Answer 1

Resposta: primeira alternativa.

Explicação passo-a-passo:

$\tt \dfrac{3\pi}{5}\ rad=\dfrac{3\pi}{5}\cdot 1=\dfrac{3\:\!\diagdown\!\!\!\!\pi}{5}\cdot \dfrac{180^\circ}{\diagdown\!\!\!\!\pi}=3\cdot \dfrac{180^\circ}{5}=3\cdot 36^\circ=\boxed{\tt 108^\circ}$

$\tt 240^\circ=240^\circ\cdot 1=240^\circ\cdot \dfrac{\pi}{180^\circ}=24\,\cdot\dfrac{\pi}{18}=4\cdot \diagup\!\!\!\!6\cdot\dfrac{\pi}{\diagup\!\!\!\!6\cdot3}=\boxed{\tt \dfrac{4\pi}{3}\ rad}$