Question

transforme os ângulos abaixo para radianos
a)120 graus
b)270 graus
c)45 graus
d)160 graus

Answer 1

Pela formula:

$\dfrac{ \alpha }{180} = \dfrac{x}{ \pi \ rad}$

Onde:
α = ângulo dado
x = radianos (encontrar)

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$a) \\ \\ \dfrac{ \alpha }{180} = \dfrac{x}{ \pi \ rad} \\ \\ \\ \dfrac{120}{180} = \dfrac{x}{ \pi \ rad} \\ \\ \\ \dfrac{2}{3} = \dfrac{x}{ \pi \ rad} \\ \\ \\ 3x = 2 \ \pi \ rad \\ \\ \\ x = \dfrac{2}{3} \ \pi \ rad$

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$b) \\ \\ \dfrac{ \alpha }{180} = \dfrac{x}{ \pi \ rad} \\ \\ \\ \dfrac{270}{180} = \dfrac{x}{ \pi \ rad} \\ \\ \\ \dfrac{3 }{2} = \dfrac{x}{ \pi \ rad} \\ \\ \\ 2x = 3 \ \pi \ rad \\ \\ \\ \\ x = \frac{3}{2} \ \pi \ rad$

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$c) \\ \\ \dfrac{ \alpha }{180} = \dfrac{x}{ \pi \ rad} \\ \\ \\ \dfrac{ 45 }{180} = \dfrac{x}{ \pi \ rad} \\ \\ \\ \dfrac{ 1 }{4} = \dfrac{x}{ \pi \ rad} \\ \\ \\ 4x = \pi \ rad \\ \\ \\ x = \dfrac{ \pi \ }{4} \ rad$

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$d) \\ \\ \dfrac{ \alpha }{180} = \dfrac{x}{ \pi \ rad} \\ \\ \\ \dfrac{ 160 }{180} = \dfrac{x}{ \pi \ rad} \\ \\ \\ \dfrac{ 8 }{9} = \dfrac{x}{ \pi \ rad} \\ \\ \\ 9x = 8 \ \pi \ rad \\ \\ \\ x = \dfrac{8}{9} \ \pi \ rad$