document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=969721>Question 969721</A>: <I><SPAN STYLE=\"word-break: break-all;\"> For the equation <BR>\n" );
document.write( "sin(8 x) = 0.97\r<BR>\n" );
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document.write( "find the smallest solution, the largest solution and the number of solutions for x in the interval 0 &#8804; x &#8804; 2&#960;.\r<BR>\n" );
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document.write( "The first two answers should be given accurate to two decimal places.\r<BR>\n" );
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document.write( "My answers (not correct) were:<BR>\n" );
document.write( "0.12<BR>\n" );
document.write( "5.77<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #592496 by </B><A HREF=/tutors/aboutme.mpl?userid=Theo><B>Theo(13342)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Theo><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.algebra.com/cgi-bin/show-face.mpl?user=Theo><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=592496\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> you have sin(8x) = .97<BR>\n" );
document.write( "the period of 8x is equal to 2pi/8.<BR>\n" );
document.write( "there will be 8 repetititions of a full sine wave sycle in a standard 0 to 2pi interval.\r<BR>\n" );
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document.write( "use your calculator to find that sin(8x) = .97 leads to an angle of 8x = 1.325230809.\r<BR>\n" );
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document.write( "since sine is positive in the first and second quadrant, than you need to get the angle in the second quadrant as well.\r<BR>\n" );
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document.write( "that angle sill be pi - 1.325230809 = 1.816361844.\r<BR>\n" );
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document.write( "those angles are 8x.\r<BR>\n" );
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document.write( "you want angles of x.\r<BR>\n" );
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document.write( "divide those angles by 8 and you will get:\r<BR>\n" );
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document.write( "x1 = .1656538512<BR>\n" );
document.write( "x2 = .2270452305\r<BR>\n" );
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document.write( "those angles will repeat every full cycle of 2pi/8.\r<BR>\n" );
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document.write( "your solution is therefore equal to:\r<BR>\n" );
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document.write( "x1 = .1656538512 plus or minus k * 2pi/8.<BR>\n" );
document.write( "x2 = .2270452305 plus or minus k * 2pi/8.\r<BR>\n" );
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document.write( "your smallest angle in the interval from 0 to 2pi will be x1 = .1656538512.\r<BR>\n" );
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document.write( "your largest angle in the interval from 0 to 2pi will be x2 = .2270452305 + 7*2pi/8 = 5.724832374.\r<BR>\n" );
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document.write( "the graph below shows the function of y = sin(8x) in the interval from 0 to 2pi.<BR>\n" );
document.write( "the smallest value of x and the largest value of x where sin(x) = .97 are marked.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" src = \"http://theo.x10hosting.com/2015/051101.jpg\" alt=\"$$$\" </>\r<BR>\n" );
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document.write( " </SPAN>\n" );
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