Question

transforme radianos os seguintes graus .
45°
90°
215°
305°
122°
75°
315°
335°

Answer 1

Pela formula:
$\dfrac{ \alpha }{180} = \dfrac{x}{ \pi \ rad}$

onde:
α =  ângulo dado:

====

$45^o \\ \\ \dfrac{ 45 }{180} = \dfrac{x}{ \pi \ rad} \\ \\ \\ 180x = 45 \ \pi \ rad \\ \\ \\ x = \dfrac{45}{180} \ \pi \ rad \\ \\ \\ \dfrac{1}{4} \ \pi \ rad \\ \\ \\ \dfrac{ \pi }{4} \ rad$

====
$90^o \\ \\ \dfrac{90 }{180} = \dfrac{x}{ \pi \ rad} \\ \\ \\ 180x = 90 \ \pi \ rad \\ \\ \\ x = \dfrac{90}{180} \ \pi \ rad \\ \\ \\ \dfrac{1}{2} \ \pi \ rad \\ \\ \\ \dfrac{ \pi }{2} \ rad$

====
$215^o \\ \\ \dfrac{215}{180} = \dfrac{x}{ \pi \ rad} \\ \\ \\ 180x = 215 \ \pi \ rad \\ \\ \\ x = \dfrac{215}{180} \ \pi \ rad \\ \\ \\ \dfrac{43}{36} \ \pi \ rad$

====
$305^o \\ \\ \dfrac{305 }{180} = \dfrac{x}{ \pi \ rad} \\ \\ \\ 180x = 305 \ \pi \ rad \\ \\ \\ x = \dfrac{305}{180} \ \pi \ rad \\ \\ \\ \dfrac{61}{36} \ \pi \ rad$

=====
$122^o \\ \\ \dfrac{122}{180} = \dfrac{x}{ \pi \ rad} \\ \\ \\ 180x = 122 \ \pi \ rad \\ \\ \\ x = \dfrac{122}{180} \ \pi \ rad \\ \\ \\ \dfrac{61}{90} \ \pi \ rad$

====
$75^o \\ \\ \dfrac{75}{180} = \dfrac{x}{ \pi \ rad} \\ \\ \\ 180x = 75 \ \pi \ rad \\ \\ \\ x = \dfrac{75}{180} \ \pi \ rad \\ \\ \\ \dfrac{5}{12} \ \pi \ rad$

====
$315^o \\ \\ \dfrac{315 }{180} = \dfrac{x}{ \pi \ rad} \\ \\ \\ 180x = 315 \ \pi \ rad \\ \\ \\ x = \dfrac{315}{180} \ \pi \ rad \\ \\ \\ \dfrac{7}{4} \ \pi \ rad$

====
$335^o \\ \\ \dfrac{335}{180} = \dfrac{x}{ \pi \ rad} \\ \\ \\ 180x = 335 \ \pi \ rad \\ \\ \\ x = \dfrac{335}{180} \ \pi \ rad \\ \\ \\ \dfrac{67}{36} \ \pi \ rad$