document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=909017>Question 909017</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Given the equation sin x = &#8722;0.2, find only the solutions that are in the interval [&#8722;&#960;, 5&#960;].<BR>\n" );
document.write( "Round to nearest 0.01.\r<BR>\n" );
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document.write( "#confused. \r<BR>\n" );
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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.  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #551480 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=551480\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> there are 4 quadrants in the interval from 0 to 2pi.<BR>\n" );
document.write( "first quadrant is 0 to pi/2 (same as 0 to 90 degrees)<BR>\n" );
document.write( "second quadrant is pi/2 to pi (same as 90 degrees to 180 degrees)<BR>\n" );
document.write( "third quadrant is pi to 3pi/2 (same as 180 to 270 degrees)<BR>\n" );
document.write( "fourth quadrant is 2pi(same as 270 to 360 degrees)\r<BR>\n" );
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document.write( "once you get past 2pi, the cycle repeats itself.\r<BR>\n" );
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document.write( "your solutions will be in the interval of 0 to 2pi and then they will repeat themselves.\r<BR>\n" );
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document.write( "let's do you problem and you'll see what i mean.\r<BR>\n" );
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document.write( "if you use your calculator to find the angle whose sine is -.2, the calculator will give you an angle of -.2013579208 radians.\r<BR>\n" );
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document.write( "that angle is in the fourth quadrant.\r<BR>\n" );
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document.write( "that doesn't really help you too much.\r<BR>\n" );
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document.write( "it's better to find the angle in the first quadrant.\r<BR>\n" );
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document.write( "you do that by making the sine positive since all trig functions are positive in the first quadrant.\r<BR>\n" );
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document.write( "when you solve for sinx = .2, you get an angle of .2019579208 radians.\r<BR>\n" );
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document.write( "that becomes your reference angle.\r<BR>\n" );
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document.write( "you can use that angle to find all the other angles.\r<BR>\n" );
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document.write( "now you know the sine is negative because that what you were given.\r<BR>\n" );
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document.write( "the sine is negative in quadrants 3 and 4.\r<BR>\n" );
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document.write( "the rules for finding an angle in each quadrant are as follows:\r<BR>\n" );
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document.write( "your reference angle is in quadrant 1.\r<BR>\n" );
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document.write( "the rules for finding the angle in each quadrant are as follows:\r<BR>\n" );
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document.write( "the angle in quadrant 1 is the reference angle.<BR>\n" );
document.write( "the angle in quadrant 2 is pi minus the reference angle.<BR>\n" );
document.write( "the angle in quadrant 3 is pi plus the reference angle.<BR>\n" );
document.write( "the angle in quadrant 4 is 2pi minus the reference angle.\r<BR>\n" );
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document.write( "you want the angle in quadrant 3 and quadrant 4.\r<BR>\n" );
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document.write( "your angle in quadrant 1 is .2019579208 radians which is your reference angle.\r<BR>\n" );
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document.write( "your angle in quadrant 3 will be pi + .2019579208 radians =  3.342950574 radians\r<BR>\n" );
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document.write( "your angle in quadrant 4 will be 2pi - .2019579208 = 6.081827386 radians\r<BR>\n" );
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document.write( "your angle will be multiples of plus or minus 2pi radians until you get past the interval you are interested in.\r<BR>\n" );
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document.write( "the interval you are interested in is -pi radians to 5pi radians.\r<BR>\n" );
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document.write( "-pi radians is equal to -3.142592654 radians.\r<BR>\n" );
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document.write( "5pi radians is equal to 15.70796327 radians.\r<BR>\n" );
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document.write( "your interval of interest is from -3.142592654 radians to 15.70796327 radians.\r<BR>\n" );
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document.write( "take your angle in quadrant 2 and keep adding 2*pi until you get past 15.70796327 radians\r<BR>\n" );
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document.write( "you will get:\r<BR>\n" );
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document.write( "3.342950574 + 1*2pi = 9.626135882 radians<BR>\n" );
document.write( "3.342950574 + 2*2pi = 15.90932119 radians ***** > 15.70796327 radians\r<BR>\n" );
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document.write( "take your angle in quadrant 2 and keep subtracting 2*pi radians until you get past -3.142592654 radians.\r<BR>\n" );
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document.write( "3.342950574 - 1*2pi = -2.940234733 radians.<BR>\n" );
document.write( "3.342950574 - 2*2pi = -9.22342004 radians ***** < -3.142592654 radians\r<BR>\n" );
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document.write( "take your angle in quadrant 4 and do the same.\r<BR>\n" );
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document.write( "6.081827386 + 1*2pi = 12.36501269 radians<BR>\n" );
document.write( "6.081827386 + 2*2pi = 18.648198 radians ***** > 15.70796327 radians\r<BR>\n" );
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document.write( "6.081827386 - 1*2pi = -.2013579208 radians<BR>\n" );
document.write( "6.081827386 - 2*2pi = -6.484543228 radians ***** < -3.142592654 radians\r<BR>\n" );
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document.write( "your solutions are:\r<BR>\n" );
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document.write( "-2.940234733 radians<BR>\n" );
document.write( "-.2013579208 radians<BR>\n" );
document.write( "3.342950574 radians<BR>\n" );
document.write( "6.081827386 radians<BR>\n" );
document.write( "9.626135882 radians<BR>\n" );
document.write( "12.36501269 radians\r<BR>\n" );
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document.write( "this will be easier to see on a graph.<BR>\n" );
document.write( "any difference in the numbers you see on the graph and the numbers shown above are due to rounding.\r<BR>\n" );
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document.write( "your graph will look like this:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" src = \"http://theo.x10hosting.com/2014/100302.jpg\" alt=\"$$$\" </>\r<BR>\n" );
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document.write( " </SPAN>\n" );
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