document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1203332>Question 1203332</A>: <I><SPAN STYLE=\"word-break: break-all;\"> If sin(t)=2/3, and t is in quadrant II, find <BR>\n" );
document.write( "cos(t), sec(t), csc(t), tan(t), cot(t). </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #838805 by </B><A HREF=/tutors/aboutme.mpl?userid=math_tutor2020><B>math_tutor2020(3817)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=math_tutor2020><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/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=838805\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font color=black size=3><BR>\n" );
document.write( "I'll use the greek letter <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=theta ALIGN=MIDDLE  ALT=\"theta\"   DISABLED_style= \"max-width:90%; height:auto;\" > (pronounced \"theta\") in place of t because theta is often used in trig.\r<BR>\n" );
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document.write( "sin(theta) = 2/3<BR>\n" );
document.write( "sine = opposite/hypotenuse\r<BR>\n" );
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document.write( "We could say<BR>\n" );
document.write( "opposite = 2<BR>\n" );
document.write( "hypotenuse = 3\r<BR>\n" );
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document.write( "Draw a right triangle in quadrant Q2 (northwest quadrant)<BR>\n" );
document.write( "The reference angle theta is placed in the bottom right corner of the triangle.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=drawing%28400%2C400%2C-5%2C5%2C-5%2C5%2C%0D%0Aline%28-5-3%2C0%2C5%2B3%2C0%29%2C%0D%0Aline%280%2C-5-3%2C0%2C5%2B3%29%2C%0D%0Ared%28line%280%2C0%2C-3%2C4%29%29%2C%0D%0Ared%28line%28-3%2C4%2C-3%2C0%29%29%2C%0D%0Ared%28line%28-3%2C0%2C0%2C0%29%29%2C%0D%0Alocate%28-1%2C0.5%2Ctheta%29%2C%0D%0A%0D%0Alocate%28-4%2C2%2C%22Opp%22%29%2C%0D%0Alocate%28-2%2C-0.1%2C%22Adj%22%29%2C%0D%0Alocate%28-1.5%2C2.4%2C%22Hyp%22%29%2C%0D%0A%0D%0Alocate%28-4%2C1.5%2C%222%22%29%2C%0D%0Alocate%28-2%2C-0.6%2C%22x%22%29%2C%0D%0Alocate%28-1%2C1.9%2C%223%22%29%2C%0D%0A%0D%0Alocate%285-0.4%2C5-0.4%2C%22Q1%22%29%2C%0D%0Alocate%28-4.6%2C5-0.4%2C%22Q2%22%29%2C%0D%0Alocate%28-4.6%2C-4.6%2C%22Q3%22%29%2C%0D%0Alocate%285-0.4%2C-4.6%2C%22Q4%22%29%2C%0D%0Alocate%280.3%2C-4%2Cmatrix%281%2C2%2C%22Diagram%22%2C%22not%22%29%29%2C%0D%0Alocate%280.3%2C-4.4%2Cmatrix%281%2C2%2C%22to%22%2C%22scale%22%29%29%0D%0A%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "The unknown side adjacent is labeled x.\r<BR>\n" );
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document.write( "Use the pythagorean theorem<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5E2%2Bb%5E2+=+c%5E2 ALIGN=MIDDLE  ALT=\"a%5E2%2Bb%5E2+=+c%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=2%5E2%2Bx%5E2+=+3%5E2 ALIGN=MIDDLE  ALT=\"2%5E2%2Bx%5E2+=+3%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=4%2Bx%5E2+=+9 ALIGN=MIDDLE  ALT=\"4%2Bx%5E2+=+9\"   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+=+9-4 ALIGN=MIDDLE  ALT=\"x%5E2+=+9-4\"   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+=+5 ALIGN=MIDDLE  ALT=\"x%5E2+=+5\"   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+=+sqrt%285%29 ALIGN=MIDDLE  ALT=\"x+=+sqrt%285%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+-sqrt%285%29 ALIGN=MIDDLE  ALT=\"x+=+-sqrt%285%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "I'll go with the negative version of x to indicate we're to the left of the y axis.<BR>\n" );
document.write( "x < 0 in Q2\r<BR>\n" );
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document.write( "Here's the updated diagram<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=drawing%28400%2C400%2C-5%2C5%2C-5%2C5%2C%0D%0Aline%28-5-3%2C0%2C5%2B3%2C0%29%2C%0D%0Aline%280%2C-5-3%2C0%2C5%2B3%29%2C%0D%0Ared%28line%280%2C0%2C-3%2C4%29%29%2C%0D%0Ared%28line%28-3%2C4%2C-3%2C0%29%29%2C%0D%0Ared%28line%28-3%2C0%2C0%2C0%29%29%2C%0D%0Alocate%28-1%2C0.5%2Ctheta%29%2C%0D%0A%0D%0Alocate%28-4%2C2%2C%22Opp%22%29%2C%0D%0Alocate%28-2%2C-0.1%2C%22Adj%22%29%2C%0D%0Alocate%28-1.5%2C2.4%2C%22Hyp%22%29%2C%0D%0A%0D%0Alocate%28-4%2C1.5%2C%222%22%29%2C%0D%0Alocate%28-2%2C-0.6%2C-sqrt%285%29%29%2C%0D%0Alocate%28-1%2C1.9%2C%223%22%29%2C%0D%0A%0D%0Alocate%285-0.4%2C5-0.4%2C%22Q1%22%29%2C%0D%0Alocate%28-4.6%2C5-0.4%2C%22Q2%22%29%2C%0D%0Alocate%28-4.6%2C-4.6%2C%22Q3%22%29%2C%0D%0Alocate%285-0.4%2C-4.6%2C%22Q4%22%29%2C%0D%0Alocate%280.3%2C-4%2Cmatrix%281%2C2%2C%22Diagram%22%2C%22not%22%29%29%2C%0D%0Alocate%280.3%2C-4.4%2Cmatrix%281%2C2%2C%22to%22%2C%22scale%22%29%29%0D%0A%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "opposite = 2<BR>\n" );
document.write( "adjacent = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-sqrt%285%29 ALIGN=MIDDLE  ALT=\"-sqrt%285%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "hypotenuse = 3\r<BR>\n" );
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document.write( "Then,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=cos%28theta%29+=+adjacent%2Fhypotenuse+=+-sqrt%285%29%2F3 ALIGN=MIDDLE  ALT=\"cos%28theta%29+=+adjacent%2Fhypotenuse+=+-sqrt%285%29%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=tan%28theta%29+=+opposite%2Fadjacent+=+2%2F%28-sqrt%285%29%29+=+-2sqrt%285%29%2F5 ALIGN=MIDDLE  ALT=\"tan%28theta%29+=+opposite%2Fadjacent+=+2%2F%28-sqrt%285%29%29+=+-2sqrt%285%29%2F5\"   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=csc%28theta%29+=+hypotenuse%2Fopposite+=+3%2F2 ALIGN=MIDDLE  ALT=\"csc%28theta%29+=+hypotenuse%2Fopposite+=+3%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" > (this is the reciprocal of sine)\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sec%28theta%29+=+hypotenuse%2Fadjacent+=+3%2F%28-sqrt%285%29%29+=+-3sqrt%285%29%2F5 ALIGN=MIDDLE  ALT=\"sec%28theta%29+=+hypotenuse%2Fadjacent+=+3%2F%28-sqrt%285%29%29+=+-3sqrt%285%29%2F5\"   DISABLED_style= \"max-width:90%; height:auto;\" > (this is the reciprocal of cosine)\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=cot%28theta%29+=+adjacent%2Fopposite+=+-sqrt%285%29%2F2 ALIGN=MIDDLE  ALT=\"cot%28theta%29+=+adjacent%2Fopposite+=+-sqrt%285%29%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" > (this is the reciprocal of tangent)<BR>\n" );
document.write( "</font> </SPAN>\n" );
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