document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=863222>Question 863222</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Hi i'm not to sure if this is in the right section but hope so. I'm currently having problems with the following question.\r<BR>\n" );
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document.write( "Given a parametric curve x = 2sint, y=sin(2t) where t takes all values in R (real numbers)<BR>\n" );
document.write( "(a) Find an implicit equation of this curve by eliminating t,<BR>\n" );
document.write( "(b) Sketch this parametric curve in the xy-plane.\r<BR>\n" );
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document.write( "I'm more confused about a , I don't expect anyone to do (b) perhaps just inform me if my thoughts are correct.<BR>\n" );
document.write( "Do i set it so that 0 = arcsin(x/2) - (arcsin(y))/2 --> from setting t=t OR somewhere along the lines of x + y = 2sint + sin(2t) and it's somehow a circle.. Or am I just completely off.. Thanks to anyone who responds !! </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #520281 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=520281\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> x = 2sin(t)<BR>\n" );
document.write( "y = sin(2t)\r<BR>\n" );
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document.write( "as far as i can tell, you eliminate t by solving for t in one of the equations and then using that value of t in the other equation.\r<BR>\n" );
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document.write( "your 2 equations are:\r<BR>\n" );
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document.write( "x = 2sin(t)<BR>\n" );
document.write( "y = sin(2t)\r<BR>\n" );
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document.write( "you solve for t in the first equation.<BR>\n" );
document.write( "start with:<BR>\n" );
document.write( "x = 2sin(t)<BR>\n" );
document.write( "divide both sides by 2 to get:<BR>\n" );
document.write( "x/2 = sin(t)<BR>\n" );
document.write( "this is true if and only if arcsin(x/2) = t<BR>\n" );
document.write( "replace t with arcsin(x/2) in the second equation to get:<BR>\n" );
document.write( "y = sin(2*arcsin(x/2))<BR>\n" );
document.write( "your equations are now in terms of x and f(x).<BR>\n" );
document.write( "the equation you can graph is y = sin(2*arcsin(x/2))<BR>\n" );
document.write( "finding the domain of this equation can be a challenge.<BR>\n" );
document.write( "since the sine of an angle is between -1 and 1, this means that the arcsine of a number is only valid when the number is between -1 and 1.<BR>\n" );
document.write( "since the number is x/2, this means that x has to be between -2 and 2 only.  <BR>\n" );
document.write( "in order for x to be between -2 and 2 only, this means that t has to be between -pi/2 and pi/2 only.<BR>\n" );
document.write( "the graph of your equation is shown below:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" src = \"http://theo.x10hosting.com/2014/apr142.jpg\" alt=\"$$$\" </><BR>\n" );
document.write( "the same graph with associated data table created in Excel is shown below:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" src = \"http://theo.x10hosting.com/2014/apr143.jpg\" alt=\"$$$\" </>\r<BR>\n" );
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document.write( "a decent reference on parametric equations is shown below:<BR>\n" );
document.write( "<a  rel=nofollow HREF= \"http://tutorial.math.lamar.edu/Classes/CalcII/ParametricEqn.aspx\" target = \"_blank\">http://tutorial.math.lamar.edu/Classes/CalcII/ParametricEqn.aspx</a>\r<BR>\n" );
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document.write( " </SPAN>\n" );
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