document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=901689>Question 901689</A>: <I><SPAN STYLE=\"word-break: break-all;\"> 16sin^2(theta)-12=0<BR>\n" );
document.write( "what are the solutions on the interval: 0 is less than or equal to theta is less than 2pi </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #546900 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=546900\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> 16 * sin^2(theta) - 12 = 0<BR>\n" );
document.write( "add 12 to both sides to get:<BR>\n" );
document.write( "16 * sin^2(theta) = 12<BR>\n" );
document.write( "divide both sides by 16 to get:<BR>\n" );
document.write( "sin^2(theta) = 12/16 = 3/4<BR>\n" );
document.write( "take the square root of both sides to get:<BR>\n" );
document.write( "sin(theta) = plus or minus sqrt(3)/2\r<BR>\n" );
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document.write( "sin(60) = sqrt(3)/2<BR>\n" );
document.write( "60 degrees is therefore your reference angle.\r<BR>\n" );
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document.write( "if sin(theta) is positive, x can be in quadrant 1 or quadrant 2.<BR>\n" );
document.write( "this makes theta equal to 60 degrees or 120 degrees.<BR>\n" );
document.write( "60 degrees in the first quadrant is 60 degrees.<BR>\n" );
document.write( "60 degrees in the second quadrant is 180 - 60 = 120 degrees.\r<BR>\n" );
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document.write( "if sin(theta) is negative, then x will be in quadrant 3 or quadrant 4.<BR>\n" );
document.write( "this makes theta equal to 240 degrees or 300 degrees.<BR>\n" );
document.write( "60 degrees in the third quadrant is equal to 180 + 60 = 240 degrees.<BR>\n" );
document.write( "60 degrees in the fourth quadrant is equal to 360 - 60 = 300 degrees.\r<BR>\n" );
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document.write( "since 2pi is equivalent to 360 degrees, your solution in the interval from 0 to 2pi is the same as your solution in the interval from 0 to 360 degrees.\r<BR>\n" );
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document.write( "the solutions in the interval from 0 to 360 degrees is:\r<BR>\n" );
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document.write( "x = 60, 120, 240, or 300 degrees.\r<BR>\n" );
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document.write( "since radians is equal to degrees * pi / 180, your equivalent solution in the interval from 0 to 2pi radians is:\r<BR>\n" );
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document.write( "x = pi/3, 2pi/3, 4pi/3, 5pi/3 radians.\r<BR>\n" );
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document.write( "a graph of y = sin(x) intersecting with the graph of y = plus or minus sqrt(3)/2 is shown below:\r<BR>\n" );
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document.write( "this graph is shown in radians.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" src = \"http://theo.x10hosting.com/2014/091503.jpg\" alt=\"$$$\" </>\r<BR>\n" );
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document.write( " </SPAN>\n" );
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