Resposta:
a)
[tex]\begin{array}{ccc}\mbox{ \sf grau ($\circ$) } & & \text{ \sf radiano (rad)} \\\sf 180^\circ & \to & \sf\pi rad \\\sf x & \to & \sf \dfrac{2 \pi}{5} \: rad\end{array}[/tex]
[tex]\sf \displaystyle \dfrac{180^\circ}{x} = \dfrac{\pi \: rad}{\dfrac{2\pi}{5}\: rad }[/tex]
[tex]\sf \displaystyle \dfrac{180^\circ}{x} = \dfrac{1}{\dfrac{2}{5} }[/tex]
[tex]\sf \displaystyle x = 180^\circ \cdot \dfrac{2}{5}[/tex]
[tex]\sf \displaystyle x = \dfrac{360^\circ}{5}[/tex]
[tex]\boxed{ \boxed { \boldsymbol{ \sf \displaystyle x = 72^\circ }}} \quad \gets \mathbf{ Resposta }[/tex]
Logo
[tex]\sf \textstyle \dfrac{2 \pi}{5} \: rad = 72^\circ[/tex]
b)
[tex]\sf \displaystyle \dfrac{9\pi}{4} \: rad = \dfrac{9 \cdot 180^\circ}{4} = \dfrac{1620^\circ}{4} =405^\circ[/tex]
C)
[tex]\sf \displaystyle \dfrac{\pi}{12} \: rad = \dfrac{180^\circ}{12} = 15^\circ[/tex]
Explicação passo-a-passo:
