Question

Transforme as medidas em radianos.

Answer 1

Olá



Para transformar, basta aplicar uma regra de simples. Para isso, usaremos a uma base (medida) conhecida.


Sabemos que π equivale a 180º no ciclo trigonométrico. Essa será nossa base.


Sempre pensaremos dessa maneira:

Se π vale 180, então a medida dada pela questão vale X.

Vamos escrever isso, resolvendo o item A)



A)


$\displaystyle\mathsf{\pi~~~~~ \longleftrightarrow~~~~~180}\\\\\mathsf{ \frac{5\pi}{4} ~~~ \longleftrightarrow~~~~~~x}$


Agora, basta multiplicar em cruz.

Não se preocupe com o π, ele irá se cancelar no final da conta.


$\displaystyle\mathsf{\pi x~=~180\cdot \frac{5\pi}{4} }\\\\\\\mathsf{\pi x~=~225\pi}$


Isola o x, passando o π para o outro lado dividindo.


$\displaystyle\mathsf{ x~=~ \frac{225\diagup\!\!\!\!\pi}{\diagup\!\!\!\!\pi} }\\\\\\\\\boxed{\mathsf{x~=~225^o}}$



Como o procedimento é o mesmo, irei fazer as contas direto para os próximos itens.





B)

$\displaystyle\mathsf{\pi~~~~~ \longleftrightarrow~~~~~180}\\\\\mathsf{ \frac{7\pi}{3} ~~~ \longleftrightarrow~~~~~~x}\\\\\\\\\\\\\mathsf{\pi x~=~180\cdot \frac{7\pi}{3} }\\\\\\\mathsf{\pi x~=~420\pi}\\\\\\\mathsf{x~=~ \frac{420\diagup\!\!\!\!\pi}{\diagup\!\!\!\!\pi} }\\\\\\\\\boxed{\mathsf{x~=~420^o}}$






C)

$\displaystyle\mathsf{\pi~~~~~ \longleftrightarrow~~~~~180}\\\\\mathsf{ \frac{9\pi}{6} ~~~ \longleftrightarrow~~~~~~x}\\\\\\\\\\\\\mathsf{\pi x~=~180\cdot \frac{9\pi}{6} }\\\\\\\mathsf{\pi x~=~270\pi}\\\\\\\mathsf{x~=~ \frac{270\diagup\!\!\!\!\pi}{\diagup\!\!\!\!\pi} }\\\\\\\\\boxed{\mathsf{x~=~270^o}}$





D)

$\displaystyle\mathsf{\pi~~~~~ \longleftrightarrow~~~~~180}\\\\\mathsf{ \frac{3\pi}{5} ~~~ \longleftrightarrow~~~~~~x}\\\\\\\\\\\\\mathsf{\pi x~=~180\cdot \frac{3\pi}{5} }\\\\\\\mathsf{\pi x~=~108\pi}\\\\\\\mathsf{x~=~ \frac{108\diagup\!\!\!\!\pi}{\diagup\!\!\!\!\pi} }\\\\\\\\\boxed{\mathsf{x~=~108^o}}$





E)

$\displaystyle\mathsf{\pi~~~~~ \longleftrightarrow~~~~~180}\\\\\mathsf{ \frac{2\pi}{6} ~~~ \longleftrightarrow~~~~~~x}\\\\\\\\\\\\\mathsf{\pi x~=~180\cdot \frac{2\pi}{6} }\\\\\\\mathsf{\pi x~=~60\pi}\\\\\\\mathsf{x~=~ \frac{60\diagup\!\!\!\!\pi}{\diagup\!\!\!\!\pi} }\\\\\\\\\boxed{\mathsf{x~=~60^o}}$




Dúvidas? Deixe nos comentários.



Dica: Quer aprender de verdade? Veja o passo a passo do item A) e em seguida tente fazer os outros sozinho.