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what is x in sin x =.5

Guest Feb 17, 2017

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 #2
avatar+18605 
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what is x in sin x =.5

 

\(\begin{array}{|rcll|} \hline \sin(x) &=& 0.5 \\ x_1 &=& \arcsin(0.5) + z\cdot 360^{\circ} \quad & | \quad z \in Z \\ \mathbf{x_1} &\mathbf{=}& \mathbf{30^{\circ} + z\cdot 360^{\circ}} \\\\ \sin(x)=\sin(180^{\circ}-x) &=& 0.5 \\ 180^{\circ}-x_2 &=& \arcsin(0.5) + z\cdot 360^{\circ} \quad & | \quad z \in Z \\ x_2 &=& 180^{\circ}- \arcsin(0.5) + z\cdot 360^{\circ} \\ x_2 &=& 180^{\circ}- 30^{\circ} + z\cdot 360^{\circ} \\ \mathbf{x_2} &\mathbf{=}&\mathbf{ 150^{\circ} + z\cdot 360^{\circ}} \\ \hline \end{array} \)

 

 

laugh

heureka  Feb 17, 2017
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 #1
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x = arcsin(.5)

asin(.5) = 30 degrees

ElectricPavlov  Feb 17, 2017
 #2
avatar+18605 
+10
Best Answer

what is x in sin x =.5

 

\(\begin{array}{|rcll|} \hline \sin(x) &=& 0.5 \\ x_1 &=& \arcsin(0.5) + z\cdot 360^{\circ} \quad & | \quad z \in Z \\ \mathbf{x_1} &\mathbf{=}& \mathbf{30^{\circ} + z\cdot 360^{\circ}} \\\\ \sin(x)=\sin(180^{\circ}-x) &=& 0.5 \\ 180^{\circ}-x_2 &=& \arcsin(0.5) + z\cdot 360^{\circ} \quad & | \quad z \in Z \\ x_2 &=& 180^{\circ}- \arcsin(0.5) + z\cdot 360^{\circ} \\ x_2 &=& 180^{\circ}- 30^{\circ} + z\cdot 360^{\circ} \\ \mathbf{x_2} &\mathbf{=}&\mathbf{ 150^{\circ} + z\cdot 360^{\circ}} \\ \hline \end{array} \)

 

 

laugh

heureka  Feb 17, 2017

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