document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1157772>Question 1157772</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Write the following polar equations in Cartesian form.<BR>\n" );
document.write( "a) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=r%5E2 ALIGN=MIDDLE  ALT=\"r%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >= 7<BR>\n" );
document.write( "b) θ = 4pi/3<BR>\n" );
document.write( "c) θ = 7pi/4<BR>\n" );
document.write( "d) r = cosθ<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #780728 by </B><A HREF=/tutors/aboutme.mpl?userid=MathLover1><B>MathLover1(20849)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=MathLover1><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=MathLover1><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=780728\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> \r<BR>\n" );
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document.write( "a) \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=r%5E2=+7 ALIGN=MIDDLE  ALT=\"r%5E2=+7\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "using the formulae that link Polar to Cartesian coordinates:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=r%5E2=x%5E2%2By%5E2 ALIGN=MIDDLE  ALT=\"r%5E2=x%5E2%2By%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2%2By%5E2=7 ALIGN=MIDDLE  ALT=\"x%5E2%2By%5E2=7\"   DISABLED_style= \"max-width:90%; height:auto;\" >-> rectangular form\r<BR>\n" );
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document.write( "b) \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=theta=+4pi%2F3 ALIGN=MIDDLE  ALT=\"theta=+4pi%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Take the tangent of both sides:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=tan%28theta%29=+tan%284pi%2F3%29 ALIGN=MIDDLE  ALT=\"tan%28theta%29=+tan%284pi%2F3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Substitute <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=tan%28theta%29=y%2Fx ALIGN=MIDDLE  ALT=\"tan%28theta%29=y%2Fx\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y%2Fx=+tan%284pi%2F3%29 ALIGN=MIDDLE  ALT=\"y%2Fx=+tan%284pi%2F3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Multiply both sides by <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x ALIGN=MIDDLE  ALT=\"x\"   DISABLED_style= \"max-width:90%; height:auto;\" >:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=+tan%284pi%2F3%29%2Ax ALIGN=MIDDLE  ALT=\"y=+tan%284pi%2F3%29%2Ax\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Substitute <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=tan%284pi%2F3%29=sqrt%283%29 ALIGN=MIDDLE  ALT=\"tan%284pi%2F3%29=sqrt%283%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=sqrt%283%29%2Ax ALIGN=MIDDLE  ALT=\"y=sqrt%283%29%2Ax\"   DISABLED_style= \"max-width:90%; height:auto;\" >-> rectangular form\r<BR>\n" );
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document.write( "c) \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=theta+=+7pi%2F4 ALIGN=MIDDLE  ALT=\"theta+=+7pi%2F4\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=tan%28theta%29+=+tan%287pi%2F4%29 ALIGN=MIDDLE  ALT=\"tan%28theta%29+=+tan%287pi%2F4%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y%2Fx=+tan%287pi%2F4%29 ALIGN=MIDDLE  ALT=\"y%2Fx=+tan%287pi%2F4%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y%2Fx=+-1 ALIGN=MIDDLE  ALT=\"y%2Fx=+-1\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=+-x ALIGN=MIDDLE  ALT=\"y=+-x\"   DISABLED_style= \"max-width:90%; height:auto;\" >-> rectangular form\r<BR>\n" );
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document.write( "d) \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=r+=+cos%28theta%29 ALIGN=MIDDLE  ALT=\"r+=+cos%28theta%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "using the formulae that link Polar to Cartesian coordinates:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=r%5E2=x%5E2%2By%5E2 ALIGN=MIDDLE  ALT=\"r%5E2=x%5E2%2By%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=r%2Acos%28theta%29+ ALIGN=MIDDLE  ALT=\"x=r%2Acos%28theta%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" >and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=r%2Asin%28theta%29 ALIGN=MIDDLE  ALT=\"y=r%2Asin%28theta%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "for this question given  : <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=r=cos%28theta%29 ALIGN=MIDDLE  ALT=\"r=cos%28theta%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > => <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=r=x%2Fr ALIGN=MIDDLE  ALT=\"r=x%2Fr\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "multiply both sides by <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=r ALIGN=MIDDLE  ALT=\"r\"   DISABLED_style= \"max-width:90%; height:auto;\" >:  => <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=r%2Ar=xr%2Fr ALIGN=MIDDLE  ALT=\"r%2Ar=xr%2Fr\"   DISABLED_style= \"max-width:90%; height:auto;\" > => <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=r%5E2=x ALIGN=MIDDLE  ALT=\"r%5E2=x\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "=> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2%2By%5E2=x ALIGN=MIDDLE  ALT=\"x%5E2%2By%5E2=x\"   DISABLED_style= \"max-width:90%; height:auto;\" >-> rectangular form\r<BR>\n" );
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