document.write( "Question 1203148: Hello. I am unsure how to solve this:
\n" ); document.write( "What is the smallest positive number for
\n" ); document.write( "3sin(2x-6)=1\r
\n" ); document.write( "\n" ); document.write( "the correct answer is: 0.028328455 (i looked it up on google). \r
\n" ); document.write( "\n" ); document.write( "To solve this problem, i brought over the 3. so the equation would become sin(2x-6)=1/3. Then i brought the sin to the right side so the equation looked like this 2x-6=sin^-1(1/3). then i carried the 6 over so it became 2x=(sin^-1(1/3))+6 and then i divided the whole equation on the left side by 2 so i can solve for x. However, by doing so, it gave me an answer of about 12.7356\r
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Algebra.Com's Answer #838481 by ikleyn(52908) $\"\"$ $\"About$

You can put this solution on YOUR website!
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document.write( "3*sin(2x-6) = 1  --->\r\n" );
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document.write( "sin(2x-6) = 1/3\r\n" );
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document.write( "2x-6 = arcsin(1/3) = 0.339837  or  2x-6 =  - arcsin(1/3) = 3.14159 - 0.339837 = 2.801753.\r\n" );
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document.write( "2x = 0.339837 + 6 = 6.339837   or  2x = 2.801753 + 6 = 8.802.\r\n" );
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document.write( "From this value of 2x = 6.339837 we can (and, therefore, we should) subtract  as many times, \r\n" );
document.write( "until we still get a positive number.\r\n" );
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document.write( "    6.339837 - 2*3.14159 = 0.056657.\r\n" );
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document.write( "It is the other, still valid candidate for 2x: geometrically, \r\n" );
document.write( "it represents THE SAME ANGLE (in radians) as 2x = 6.339837.\r\n" );
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document.write( "    +---------------------------------------------------------------------+\r\n" );
document.write( "    |  In other words, we can say that the angle of 2x = 6.339837 radians |\r\n" );
document.write( "    |       is equivalent to the angle of 0.056657 radians.               |\r\n" );
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document.write( "So, to get x, we divide the value of 0.056657 by 2\r\n" );
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document.write( "     = 0.0283285 radians,\r\n" );
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document.write( "which is close to the answer.\r\n" );
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\n" ); document.write( "\n" ); document.write( "The lesson to learn from my post is this:\r
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document.write( "    Geometrically, the numbers in radians, that are different \r\n" );
document.write( "    by the value of , represent the  SAME  ANGLE.\r\n" );
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document.write( "    So, for us such numbers, representing angles, are equivalent.\r\n" );
document.write( "    This understanding is a key for solving this problem and many other similar problems.\r\n" );
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\n" ); document.write( "\n" ); document.write( "Alternatively, you may look into my other (very similar) solution to this problem\r
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\n" ); document.write( "\n" ); document.write( "https://www.algebra.com/algebra/homework/logarithm/logarithm.faq.question.1188985.html\r
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\n" ); document.write( "\n" ); document.write( "which I provided at this forum several years ago.\r
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