Question

Em cada item , expressem a medida em radianos :

a 30° b 245° c 96° d 72° f 320° e 216°30`

Answer 1

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

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a)

$\dfrac{ 30}{180} = \dfrac{x}{ \pi \ rad} \\ \\ \\ \dfrac{ 1}{6} = \dfrac{x}{ \pi \ rad} \\ \\ \\ 6x = 1* \pi \ rad \\ \\ \\ x = \dfrac{ \pi }{6} \ rad$

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b)

$\dfrac{245}{180} = \dfrac{x}{ \pi \ rad} \\ \\ \\ \dfrac{ 49}{36} = \dfrac{x}{ \pi \ rad} \\ \\ \\ 36x = 49* \pi \ rad \\ \\ \\ x = \dfrac{ 49\ \pi }{36} \ rad$

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c)

$\dfrac{ 96}{180} = \dfrac{x}{ \pi \ rad} \\ \\ \\ \dfrac{8}{15} = \dfrac{x}{ \pi \ rad} \\ \\ \\ 15x = 8* \pi \ rad \\ \\ \\ x = \dfrac{ 8\ \pi }{15} \ rad$

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d)

$\dfrac{72}{180} = \dfrac{x}{ \pi \ rad} \\ \\ \\ \dfrac{2}{5} = \dfrac{x}{ \pi \ rad} \\ \\ \\ 5x = 2* \pi \ rad \\ \\ \\ x = \dfrac{ 2 \ \pi }{5} \ rad$

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e)

$\dfrac{ 216,30}{180} = \dfrac{x}{ \pi \ rad} \\ \\ \\ 1,20 = \dfrac{x}{ \pi \ rad} \\ \\ \\ x \approx 1,20 \ \pi \ rad$

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f)

$\dfrac{320}{180} = \dfrac{x}{ \pi \ rad} \\ \\ \\ \dfrac{16}{9} = \dfrac{x}{ \pi \ rad} \\ \\ \\ 9x = 16 * \pi \ rad \\ \\ \\ x = \dfrac{ 16 \ \pi }{9} \ rad$