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# Sin(3x)=-0.6

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864
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Sin(3x)=-0.6

May 14, 2015

#2
+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
+95369
+5

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

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

Here is a graphical solution

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

May 14, 2015
#2
+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...

heureka May 14, 2015
#3
+95369
0

I think our answers are probably the same Heureka

May 14, 2015