Question

Transformers os números abaixo para grau as seguintes medidas de arco

Answer 1

Resposta:

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Answer 2

Resposta:

a)

$\begin{array}{ccc}\mbox{ \sf grau ( \circ ) } & & \text{ \sf radiano (rad)} \\\sf 180^\circ & \to & \sf\pi rad \\\sf x & \to & \sf \dfrac{2 \pi}{5} \: rad\end{array}$

$\sf \displaystyle \dfrac{180^\circ}{x} = \dfrac{\pi \: rad}{\dfrac{2\pi}{5}\: rad }$

$\sf \displaystyle \dfrac{180^\circ}{x} = \dfrac{1}{\dfrac{2}{5} }$

$\sf \displaystyle x = 180^\circ \cdot \dfrac{2}{5}$

$\sf \displaystyle x = \dfrac{360^\circ}{5}$

$\boxed{ \boxed { \boldsymbol{ \sf \displaystyle x = 72^\circ }}} \quad \gets \mathbf{ Resposta }$

Logo

$\sf \textstyle \dfrac{2 \pi}{5} \: rad = 72^\circ$

b)

$\sf \displaystyle \dfrac{9\pi}{4} \: rad = \dfrac{9 \cdot 180^\circ}{4} = \dfrac{1620^\circ}{4} =405^\circ$

C)

$\sf \displaystyle \dfrac{\pi}{12} \: rad = \dfrac{180^\circ}{12} = 15^\circ$

Explicação passo-a-passo: