Question 1203148
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<pre>

3*sin(2x-6) = 1  --->


sin(2x-6) = 1/3


2x-6 = arcsin(1/3) = 0.339837  or  2x-6 = {{{pi}}} - arcsin(1/3) = 3.14159 - 0.339837 = 2.801753.


2x = 0.339837 + 6 = 6.339837   or  2x = 2.801753 + 6 = 8.802.


From this value of 2x = 6.339837 we can (and, therefore, we should) subtract {{{2pi}}} as many times, 
until we still get a positive number.

    6.339837 - 2*3.14159 = 0.056657.


It is the other, still valid candidate for 2x: geometrically, 
it represents THE SAME ANGLE (in radians) as 2x = 6.339837.


    +---------------------------------------------------------------------+
    |  In other words, we can say that the angle of 2x = 6.339837 radians |
    |       is equivalent to the angle of 0.056657 radians.               |
    +---------------------------------------------------------------------+


So, to get x, we divide the value of 0.056657 by 2

    {{{0.056657/2}}} = 0.0283285 radians,

which is close to the answer.
</pre>

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The lesson to learn from my post is this:


<pre>
    Geometrically, the numbers in radians, that are different 
    by the value of {{{2pi}}}, represent the  SAME  ANGLE.

    So, for us such numbers, representing angles, are equivalent.
    This understanding is a key for solving this problem and many other similar problems.
</pre>


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Alternatively, you may look into my other (very similar) solution to this problem


https://www.algebra.com/algebra/homework/logarithm/logarithm.faq.question.1188985.html


which I provided at this forum several years ago.