document.write( "Question 909017: Given the equation sin x = −0.2, find only the solutions that are in the interval [−π, 5π].
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\n" ); document.write( "\n" ); document.write( "Im plugged that into my calculator and gotten. x=-.20 in radians. However the interval part of the question is throwing me off. \n" ); document.write( "

Algebra.Com's Answer #551474 by Edwin McCravy(20081) $\"\"$ $\"About$

You can put this solution on YOUR website!

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document.write( "You can't go by what the calculator gives for sin^-1 unless\r\n" );
document.write( "you want only the answer between  and .\r\n" );
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document.write( "Also it's better not to round off until the end.\r\n" );
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document.write( "What you do is fisrt find sin^-1 of POSITIVE 0.2 which will\r\n" );
document.write( "give the QI answer of .2013579209, which is not a solution, but only\r\n" );
document.write( "the reference angle in radians.  \r\n" );
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document.write( "First let's find the positive values, then we'll find the negative values.\r\n" );
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document.write( "We know that the sine is negative only in QIII and QIV,  So to get the \r\n" );
document.write( "first positive QIII answer we add  to the reference angle to get\r\n" );
document.write( "3.342950574.  To get the first QIV answer we subtract the reference angle\r\n" );
document.write( "from  and get 6.081827386.\r\n" );
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document.write( "So the first two positive solutions are 3.342950574 and 6.081827386\r\n" );
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document.write( "Now we begin adding  to each of those and get as many answers\r\n" );
document.write( "as we can that don't exceed  which is 15.70796327.\r\n" );
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document.write( "Adding  to 3.342950574 and 6.081827386 gives\r\n" );
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document.write( "                    9.626135882 and 12.36501269\r\n" );
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document.write( "Adding  to those gives\r\n" );
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document.write( "                   15.90932119 and 18.648198, but both are too large.\r\n" );
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document.write( "So all the positive solutions are\r\n" );
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document.write( "3.342950574, 6.081827386, 9.626135882 and 12.36501269.\r\n" );
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document.write( "Now let's find the negative solutions.\r\n" );
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document.write( "We go bact to the first two positive solutions, 3.342950574 and 6.081827386\r\n" );
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document.write( "Now we begin subtracting  from each of those and get as many \r\n" );
document.write( "negative solutions as we can that don't go below  which is \r\n" );
document.write( "-3.141592654.\r\n" );
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document.write( "Subtracting  from 3.342950574 and 6.081827386 gives\r\n" );
document.write( "                        -2.940234733 and -.2013579208\r\n" );
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document.write( "Subtracting  from those gives\r\n" );
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document.write( "                       -9.22342004 and -6.484543228 both too small.\r\n" );
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document.write( "So all the solutions are, smallest to largest:\r\n" );
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document.write( "       -2.94, -0.20, 3.34, 6.08, 9.63, 12.37 \r\n" );
document.write( "                           \r\n" );
document.write( "Edwin

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