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Sin(3x)=-0.6

 May 14, 2015

Best Answer 

 #2
avatar+20852 
+5

Sin(3x)=-0.6         x = ?

 

$$\small{\text{$
\begin{array}{|lrcl|lrcl|}
\hline
I.& &&& II. &\\
&&&& \boxed{\sin{(\alpha)} = \sin{(180\ensurement{^{\circ}}-\alpha)} }\\
\hline
& && && && \\
&\sin(3x) &=& -0.6 && \sin(180\ensurement{^{\circ}} -3x) &=& -0.6 \\
& && && && \\
&3x &=& \arcsin{(-0.6)} && 180\ensurement{^{\circ}} -3x &=& \arcsin{(-0.6)} \\
& && && && \\
&x &=& \dfrac{ \arcsin{(-0.6)}}{3} && 3x &=& 180\ensurement{^{\circ}} -\arcsin{(-0.6)} \\
& && && && \\
&x &=& -12.2899658819\ensurement{^{\circ}} \pm k\cdot 360\ensurement{^{\circ}} && x &=& \dfrac{ 180\ensurement{^{\circ}} -\arcsin{(-0.6)} }{3} \\
& && && && \\
& && && x &=& 72.2899658819\ensurement{^{\circ}} \pm k\cdot 360\ensurement{^{\circ}} \\
& && && && \\
\hline
\end{array}
$}}$$

k = 1,2, 3...

 May 14, 2015
 #1
avatar+95369 
+5

$$\underset{\,\,\,\,^{\textcolor[rgb]{0.66,0.66,0.66}{360^\circ}}}{{sin}}^{\!\!\mathtt{-1}}{\left({\mathtt{0.6}}\right)} = {\mathtt{36.869\: \!897\: \!645\: \!844^{\circ}}}$$

 

 

$$\\3x=180+37, \;\; 360-37,.....\\\\
x=60+(37/3), \;\; 120-(37/3), .....\\\\
x=60n+(-1)^{(n+1)}(37/3)\qquad n\in Z\\\\
x=60n+(-1)^{(n+1)}(12)\qquad n\in Z \qquad $to the closest degrees$$$

 

Here is a graphical solution   

 

https://www.desmos.com/calculator/gsoviecfsi

 May 14, 2015
 #2
avatar+20852 
+5
Best Answer

Sin(3x)=-0.6         x = ?

 

$$\small{\text{$
\begin{array}{|lrcl|lrcl|}
\hline
I.& &&& II. &\\
&&&& \boxed{\sin{(\alpha)} = \sin{(180\ensurement{^{\circ}}-\alpha)} }\\
\hline
& && && && \\
&\sin(3x) &=& -0.6 && \sin(180\ensurement{^{\circ}} -3x) &=& -0.6 \\
& && && && \\
&3x &=& \arcsin{(-0.6)} && 180\ensurement{^{\circ}} -3x &=& \arcsin{(-0.6)} \\
& && && && \\
&x &=& \dfrac{ \arcsin{(-0.6)}}{3} && 3x &=& 180\ensurement{^{\circ}} -\arcsin{(-0.6)} \\
& && && && \\
&x &=& -12.2899658819\ensurement{^{\circ}} \pm k\cdot 360\ensurement{^{\circ}} && x &=& \dfrac{ 180\ensurement{^{\circ}} -\arcsin{(-0.6)} }{3} \\
& && && && \\
& && && x &=& 72.2899658819\ensurement{^{\circ}} \pm k\cdot 360\ensurement{^{\circ}} \\
& && && && \\
\hline
\end{array}
$}}$$

k = 1,2, 3...

heureka May 14, 2015
 #3
avatar+95369 
0

I think our answers are probably the same Heureka   

 May 14, 2015

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