Question

4) Converta os ângulos de graus para radianos. (use regra de três)
a) 60°=
b)45°=
c)210°=
d)300°=
e)130°=
f)150°=
g)270°=
h)135°=​

Answer 1

$\boxed{\begin{array}{l}\tt a)~\sf \pi\,rad\longrightarrow 180^\circ\\\sf x\longrightarrow 60^\circ\\\sf x=\dfrac{60\cdot\pi}{180}=\dfrac{\pi}{3}\,rad\\\tt b)~\sf \pi\,rad\longrightarrow 180^\circ\\\sf x\longrightarrow 45^\circ\\\sf x=\dfrac{45\cdot\pi}{180}=\dfrac{\pi}{4}\,rad\\\tt c)~\sf \pi\,rad\longrightarrow180^\circ\\\sf x\longrightarrow210^\circ\\\sf x=\dfrac{210\cdot\pi}{180}=\dfrac{7\pi}{6}\,rad\end{array}}$

$\boxed{\begin{array}{l}\tt d)~\sf \pi\,rad\longrightarrow 180^\circ\\\sf x\longrightarrow300^\circ\\\sf x=\dfrac{300\cdot\pi}{180}=\dfrac{5\pi}{3}\,rad\\\tt e)~\sf\pi\,rad\longrightarrow 180^\circ\\\sf x\longrightarrow 130^\circ\\\sf x=\dfrac{130\cdot\pi}{180}=\dfrac{13\pi}{18}\\\tt f)~\sf \pi\,rad\longrightarrow180^\circ\\\sf x\longrightarrow 150^\circ\\\sf x=\dfrac{150\cdot\pi}{180}=\dfrac{5\pi}{6}\,rad \end{array}}$

$\boxed{\begin{array}{l}\tt g)~\sf\pi\,rad\longrightarrow 180^\circ\\\sf x\longrightarrow 270^\circ\\\sf x=\dfrac{270\cdot\pi}{180}=\dfrac{3\pi}{2}\,rad\\\tt h)~\sf \pi\,rad\longrightarrow 180^\circ\\\sf x\longrightarrow 135^\circ\\\sf x=\dfrac{135\cdot\pi}{180}\\\sf x=\dfrac{3\pi}{4}\,rad\end{array}}$