document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1169011>Question 1169011</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Please help me Solve this equation on [0,360)<BR>\n" );
document.write( "sin^3 (x) = sin(x)<BR>\n" );
document.write( "Thank you in advance </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #793669 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=793669\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> your original equation is:\r<BR>\n" );
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document.write( "sin^3(x) = sin(x)\r<BR>\n" );
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document.write( "divide both side of the equation by sin(x) to get:\r<BR>\n" );
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document.write( "sin^2(x) = 1\r<BR>\n" );
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document.write( "take the square root of both sides of the equation to get:\r<BR>\n" );
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document.write( "sin(x) = plus or minus sqrt(1).\r<BR>\n" );
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document.write( "since sqrt(1) is equal to 1, this becomes;\r<BR>\n" );
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document.write( "sin(x) = plus or minus 1.\r<BR>\n" );
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document.write( "when sin(x) = 1, solve for x to get:\r<BR>\n" );
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document.write( "x = arcsin(1) = 90 degrees.\r<BR>\n" );
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document.write( "when sin(x) = -1, solve for x to get:\r<BR>\n" );
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document.write( "x = arcsin(-1) = -90 degrees.\r<BR>\n" );
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document.write( "what you want is the equivalent angle that is greater than 0 and less then 360 degrees.\r<BR>\n" );
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document.write( "add 360 to -90 and you get 270 degrees.\r<BR>\n" );
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document.write( "that's the angle you're looking for.\r<BR>\n" );
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document.write( "arcsin(-1) = 270 degrees.\r<BR>\n" );
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document.write( "i believe your answer will be x = 90 and 270 degrees.\r<BR>\n" );
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document.write( "the equation of sin^3(x) - sin(x) can be graphed.\r<BR>\n" );
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document.write( "to graph it, set up 4 equations.\r<BR>\n" );
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document.write( "they will be:\r<BR>\n" );
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document.write( "y = sin^3(x)<BR>\n" );
document.write( "y = sin(x)<BR>\n" );
document.write( "y = 1<BR>\n" );
document.write( "y = -1\r<BR>\n" );
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document.write( "the intersection of these 4 equations will be your solution.\r<BR>\n" );
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document.write( "the graph looks like this:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" src = \"http://theo.x10hosting.com/2020/110406.jpg\" >\r<BR>\n" );
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document.write( "note that sin^3(x) is equivalent to sin(x)^3.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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