document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=744146>Question 744146</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Please help me determine two other angles that have the same trig ratio as sin 2.3. I dont know where to begin; can i switch the radian to a degree? Please help!! </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #453221 by </B><A HREF=/tutors/aboutme.mpl?userid=KMST><B>KMST(5328)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=KMST><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=KMST><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=453221\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> You could switch radians to degrees, but that would not help if the answer is expected in radians.<BR>\n" );
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document.write( "MATCHING JUST SINE:<BR>\n" );
document.write( "The sine of supplementary angles is the same. For example,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sin%2830%5Eo%29=sin%28180%5E0-30%5Eo%29=sin%28150%5E0%29=0.5 ALIGN=MIDDLE  ALT=\"sin%2830%5Eo%29=sin%28180%5E0-30%5Eo%29=sin%28150%5E0%29=0.5\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "and all the angles differing by <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=k%2A360%5Eo ALIGN=MIDDLE  ALT=\"k%2A360%5Eo\"   DISABLED_style= \"max-width:90%; height:auto;\" > from those have the same sine too.<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2pi ALIGN=MIDDLE  ALT=\"2pi\"   DISABLED_style= \"max-width:90%; height:auto;\" > radians corresponds to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=360%5Eo ALIGN=MIDDLE  ALT=\"360%5Eo\"   DISABLED_style= \"max-width:90%; height:auto;\" >,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=pi ALIGN=MIDDLE  ALT=\"pi\"   DISABLED_style= \"max-width:90%; height:auto;\" > radians corresponds to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=180%5Eo ALIGN=MIDDLE  ALT=\"180%5Eo\"   DISABLED_style= \"max-width:90%; height:auto;\" >, and<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=pi%2F2 ALIGN=MIDDLE  ALT=\"pi%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" > radians corresponds to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=90%5Eo ALIGN=MIDDLE  ALT=\"90%5Eo\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=pi%2F2%3C2.3%3Cpi ALIGN=MIDDLE  ALT=\"pi%2F2%3C2.3%3Cpi\"   DISABLED_style= \"max-width:90%; height:auto;\" > so an angle of 2.3 radians is in the second quadrant.<BR>\n" );
document.write( "There is a supplementary first quadrant angle that has the same sine: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=pi-2.3 ALIGN=MIDDLE  ALT=\"pi-2.3\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "All the angles that differ from those by a whole number of turns (clockwise or counterclockwise) have the same sine too, so adding or subtracting <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2pi ALIGN=MIDDLE  ALT=\"2pi\"   DISABLED_style= \"max-width:90%; height:auto;\" > to the previous answers gives you more answers:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2pi%2B2.3 ALIGN=MIDDLE  ALT=\"2pi%2B2.3\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2.3-2pi ALIGN=MIDDLE  ALT=\"2.3-2pi\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3pi-2.3 ALIGN=MIDDLE  ALT=\"3pi-2.3\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-2.3-pi ALIGN=MIDDLE  ALT=\"-2.3-pi\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "If you want to translate 2.3 radians to degrees, knowing that <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=pi ALIGN=MIDDLE  ALT=\"pi\"   DISABLED_style= \"max-width:90%; height:auto;\" > radians corresponds to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=180%5Eo ALIGN=MIDDLE  ALT=\"180%5Eo\"   DISABLED_style= \"max-width:90%; height:auto;\" >, you can calculate that 2.3 radians corresponds to<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2.3%2A180%5Eo%2Fpi ALIGN=MIDDLE  ALT=\"2.3%2A180%5Eo%2Fpi\"   DISABLED_style= \"max-width:90%; height:auto;\" >= approximately <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=131.8%5Eo ALIGN=MIDDLE  ALT=\"131.8%5Eo\"   DISABLED_style= \"max-width:90%; height:auto;\" > (rounding to the nearest <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0.1%5Eo ALIGN=MIDDLE  ALT=\"0.1%5Eo\"   DISABLED_style= \"max-width:90%; height:auto;\" >)<BR>\n" );
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document.write( "IF YOU HAVE TO MATCH ALL TRIG RATIOS:<BR>\n" );
document.write( "The angles that have all the same trigonometric ratios are the co-terminal angles, those that differ by multiples of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=360%5Eo ALIGN=MIDDLE  ALT=\"360%5Eo\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2pi ALIGN=MIDDLE  ALT=\"2pi\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "So, for an angle <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=alpha ALIGN=MIDDLE  ALT=\"alpha\"   DISABLED_style= \"max-width:90%; height:auto;\" > (in degrees), all angles measuring <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=alpha%2Bk%2A360%5Eo ALIGN=MIDDLE  ALT=\"alpha%2Bk%2A360%5Eo\"   DISABLED_style= \"max-width:90%; height:auto;\" > for some positive or negative integer <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=k ALIGN=MIDDLE  ALT=\"k\"   DISABLED_style= \"max-width:90%; height:auto;\" > have all the same trigonometric  ratios.<BR>\n" );
document.write( "Thinking in radians, for an angle <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=theta ALIGN=MIDDLE  ALT=\"theta\"   DISABLED_style= \"max-width:90%; height:auto;\" > (in radians), all angles measuring <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=theta+%2Bk%2A2pi ALIGN=MIDDLE  ALT=\"theta+%2Bk%2A2pi\"   DISABLED_style= \"max-width:90%; height:auto;\" > for some positive or negative integer <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=k ALIGN=MIDDLE  ALT=\"k\"   DISABLED_style= \"max-width:90%; height:auto;\" > have all the same trigonometric  ratios. </SPAN>\n" );
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