document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1137376>Question 1137376</A>: <I><SPAN STYLE=\"word-break: break-all;\"> I need help finding the value of the trig functions\r<BR>\n" );
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document.write( "1.    Use special right triangles to state the value of the 6 trig functions for 30 degrees, 45 degrees and 60 degrees </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #755285 by </B><A HREF=/tutors/aboutme.mpl?userid=greenestamps><B>greenestamps(13206)</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=755285\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <br><BR>\n" );
document.write( "As you begin studying trigonometry, you need to be able to quickly find the values of the trig functions for these special angles.  Rote memorization is not a particularly good method; having a picture in your mind of where those angles comes from is a much more reliable method.<br><BR>\n" );
document.write( "For the 45 degree angle, think of the diagonal of a square.  If the side lengths of the square are 1, then the diagonal (by the Pythagorean Theorem) is sqrt(2).  Then<br><BR>\n" );
document.write( "sin(45) = cos(45) = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2Fsqrt%282%29+=+sqrt%282%29%2F2 ALIGN=MIDDLE  ALT=\"1%2Fsqrt%282%29+=+sqrt%282%29%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "tan(45) = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sin%2845%29%2Fcos%2845%29+=+1 ALIGN=MIDDLE  ALT=\"sin%2845%29%2Fcos%2845%29+=+1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "cot(45) = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2Ftan%2845%29+=+1%2F1+=+1 ALIGN=MIDDLE  ALT=\"1%2Ftan%2845%29+=+1%2F1+=+1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "sec(45) = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2Fcos%2845%29+=+sqrt%282%29 ALIGN=MIDDLE  ALT=\"1%2Fcos%2845%29+=+sqrt%282%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "csc(45) = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2Fsin%2845%29+=+sqrt%282%29 ALIGN=MIDDLE  ALT=\"1%2Fsin%2845%29+=+sqrt%282%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "For the 30 and 60 degree angles, think of an equilateral triangle cut in half; that forms two 30-60-90 right triangles.  If the side length of the triangle is 1, then the short side of each 30-60-90 right triangle is 1/2 (half the length of a side of the triangle).  Then the Pythagorean Theorem give us the length of the long leg of each 30-60-90 right triangle as sqrt(3)/2.  Then<br><BR>\n" );
document.write( "sin(30) = cos(60) = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%281%2F2%29%2F1+=+1%2F2 ALIGN=MIDDLE  ALT=\"%281%2F2%29%2F1+=+1%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "cos(30) = sin(60) = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28sqrt%283%29%2F2%29%2F1+=+sqrt%283%29%2F2 ALIGN=MIDDLE  ALT=\"%28sqrt%283%29%2F2%29%2F1+=+sqrt%283%29%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "tan(30) = cot(60) = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%281%2F2%29%2F%28sqrt%283%29%2F2%29+=+1%2Fsqrt%283%29+=+sqrt%283%29%2F3 ALIGN=MIDDLE  ALT=\"%281%2F2%29%2F%28sqrt%283%29%2F2%29+=+1%2Fsqrt%283%29+=+sqrt%283%29%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "csc(30) = sec(60) = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2F%281%2F2%29+=+2 ALIGN=MIDDLE  ALT=\"1%2F%281%2F2%29+=+2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "csc(60) = sec(30) = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2F%28sqrt%283%29%2F2%29+=+2%2Fsqrt%283%29 ALIGN=MIDDLE  ALT=\"1%2F%28sqrt%283%29%2F2%29+=+2%2Fsqrt%283%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "cot(30) = tan(60) = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2F%281%2Fsqrt%283%29%29+=+sqrt%283%29 ALIGN=MIDDLE  ALT=\"1%2F%281%2Fsqrt%283%29%29+=+sqrt%283%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br> </SPAN>\n" );
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