document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1103336>Question 1103336</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Solve the following equation on the interval [0, 360 degrees]: <BR>\n" );
document.write( "sin2x=1\r<BR>\n" );
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document.write( "This is what I have done so far: <BR>\n" );
document.write( "Let 2x = theta<BR>\n" );
document.write( "sin theta = 1<BR>\n" );
document.write( "theta = 90 degrees <BR>\n" );
document.write( "2x = 90 --> x = 45 degrees \r<BR>\n" );
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document.write( "Add period to theta:<BR>\n" );
document.write( "90 + 180 = 270 --> x = 270/2 = 135 degrees<BR>\n" );
document.write( "270+ 90 = 450 --> x = 450/2 = 225 degrees\r<BR>\n" );
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document.write( "I don't understand why the answer in my book says \"x = 45 degrees, 225 degrees\". According to my work done, shouldn't x = 135 degrees as well? \r<BR>\n" );
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document.write( "Help with this question would be really appreciated! </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #718053 by </B><A HREF=/tutors/aboutme.mpl?userid=greenestamps><B>greenestamps(13203)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=greenestamps><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=greenestamps><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=718053\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <br><BR>\n" );
document.write( "Well, for one thing, 135 degrees does not satisfy the equation.  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sin%282%2A135%29+=+sin%28270%29+=+-1 ALIGN=MIDDLE  ALT=\"sin%282%2A135%29+=+sin%28270%29+=+-1\"   DISABLED_style= \"max-width:90%; height:auto;\" >....<br><BR>\n" );
document.write( "The period of sine is 360 degrees, not 180 degrees.<br><BR>\n" );
document.write( "After you get your first answer of 2x=90, giving you the answer x=45 degrees, your next answer comes from 2x = 90+360 = 450, giving you the answer x=225 degrees.<br><BR>\n" );
document.write( "I suspect that your confusion comes from thinking that, since the equation involves sin(2x), you only need to add 360/2=180 degrees to your first answer for 2x.<br><BR>\n" );
document.write( "I always found it easier to avoid this kind of confusion by first solving the problem all the way through for the values of 2x and then getting my answers for x from those answers.<br><BR>\n" );
document.write( "In this problem, we are to find the solutions to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sin%282x%29=1%7D%7D+on+the+interval+%7B%7B%7B0%3C=x%3C360 ALIGN=MIDDLE  ALT=\"sin%282x%29=1%7D%7D+on+the+interval+%7B%7B%7B0%3C=x%3C360\"   DISABLED_style= \"max-width:90%; height:auto;\" >.  Since our function is sin(2x), the prescribed interval <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0%3C=x%3C360 ALIGN=MIDDLE  ALT=\"0%3C=x%3C360\"   DISABLED_style= \"max-width:90%; height:auto;\" > becomes <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0%3C=2x%3C720 ALIGN=MIDDLE  ALT=\"0%3C=2x%3C720\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<br><BR>\n" );
document.write( "So now find all the solutions between 0 and 720 degrees where the value of sine is 1; they are at 90 degrees and 450 degrees.  Then, since the values of 2x are 90 and 450 degrees, the values for x (the solutions we are to find) are 45 and 225 degrees. </SPAN>\n" );
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