How do you solve $sin(x)=1/2$ ?

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How do you solve $sin(x)=1/2$ ?

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Answer 1 · 2015-04-14T20:21:02

The solutions are:

$x=pi/6+2kpi$

and

$x=5/6pi+2kpi$ .

Draw the trigonometric circle and a line passing from $O$ with a slope of $alpha=pi/6$ . That line intercept the circle in a point $A$ , make the perpendicular from that point to the x-axis, the interception is $B$ .
The triangle $OAB$ is half of an equilater triangle with $OA=1$ and $AB=1/2$ . So $sinalpha=(AB)/(OA)=1/2$ .

You can say the same with the other line with $alpha=5/6pi$ .

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How do you solve $sin(x)=1/2$ ?

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