document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=875547>Question 875547</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Im stuck, please help me solve and go into detail <BR>\n" );
document.write( "Find the exact value<BR>\n" );
document.write( "Given that sin &#1256; = -4/5 with &#1256; in quadrant IV, find tan 2&#1256; <BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #528354 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=528354\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> With <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 quadrant IV, cosine will be positive, while sine and tangent are negative.<BR>\n" );
document.write( "That information, along with the value of one of the trigonometric functions allows you to calculate all trigonometric function values for <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=theta ALIGN=MIDDLE  ALT=\"theta\"   DISABLED_style= \"max-width:90%; height:auto;\" > ,<BR>\n" );
document.write( "and using trigonometric identities, you can calculate values for <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2theta ALIGN=MIDDLE  ALT=\"2theta\"   DISABLED_style= \"max-width:90%; height:auto;\" > too.<BR>\n" );
document.write( "The 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;\" > could be the angle AOP shown below, measuring about {{-53^o}}} .<BR>\n" );
document.write( " <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=drawing%28300%2C300%2C-1.2%2C1.2%2C-1.2%2C1.2%2C%0D%0Agrid%280%29%2Ccircle%280%2C0%2C1%29%2C%0D%0Aarrow%280%2C0%2C0.84%2C-1.12%29%2C%0D%0Alocate%280.02%2C0.13%2CO%29%2Clocate%281.02%2C0.13%2CA%29%2C%0D%0Acircle%280.6%2C-0.8%2C0.02%29%2Clocate%280.65%2C-0.74%2CP%29%2C%0D%0Alocate%280.1%2C-0.03%2Cred%28theta%29%29%2C%0D%0Atriangle%280%2C0%2C0.6%2C0%2C0.6%2C-0.8%29%2C%0D%0Arectangle%280.6%2C0%2C0.55%2C-0.05%29%2C%0D%0Alocate%280.61%2C-0.35%2C0.8%29%2Clocate%280.3%2C0.1%2Cx%5BP%5D%29%2C%0D%0Alocate%280.27%2C-0.4%2C1%29%2C%0D%0Ared%28arc%280%2C0%2C0.5%2C0.5%2C0%2C53%29%29%0D%0A%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" > I could make <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=theta=307%5Eo ALIGN=MIDDLE  ALT=\"theta=307%5Eo\"   DISABLED_style= \"max-width:90%; height:auto;\" > going from A to P the other way around,<BR>\n" );
document.write( "but if I say that <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=theta=about-53%5Eo ALIGN=MIDDLE  ALT=\"theta=about-53%5Eo\"   DISABLED_style= \"max-width:90%; height:auto;\" > ,<BR>\n" );
document.write( "or if I say <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=theta=-53%5Eo%2B360%5Eo=307%5Eo ALIGN=MIDDLE  ALT=\"theta=-53%5Eo%2B360%5Eo=307%5Eo\"   DISABLED_style= \"max-width:90%; height:auto;\" > ,<BR>\n" );
document.write( "or even <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=theta=-53%5Eo%2B2%2A360%5Eo=667%5Eo ALIGN=MIDDLE  ALT=\"theta=-53%5Eo%2B2%2A360%5Eo=667%5Eo\"   DISABLED_style= \"max-width:90%; height:auto;\" > ,<BR>\n" );
document.write( "the trigonometric functions of those angles are all the same,<BR>\n" );
document.write( "because they all have OA and OP for sides.<BR>\n" );
document.write( " <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sin%28theta%29=-4%2F5=-0.8 ALIGN=MIDDLE  ALT=\"sin%28theta%29=-4%2F5=-0.8\"   DISABLED_style= \"max-width:90%; height:auto;\" > is the y-coordinate of point P<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5BP%5D=cos%28theta%29 ALIGN=MIDDLE  ALT=\"x%5BP%5D=cos%28theta%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > is the x-coordinate of point P<BR>\n" );
document.write( "We know that the squares of sine and cosine add up to 1, so<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5BP%5D%5E2%2B%28-0.8%29%5E2=1 ALIGN=MIDDLE  ALT=\"x%5BP%5D%5E2%2B%28-0.8%29%5E2=1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5BP%5D%5E2%2B0.64=1 ALIGN=MIDDLE  ALT=\"x%5BP%5D%5E2%2B0.64=1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5BP%5D%5E2=1-0.64 ALIGN=MIDDLE  ALT=\"x%5BP%5D%5E2=1-0.64\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5BP%5D=0.6 ALIGN=MIDDLE  ALT=\"x%5BP%5D=0.6\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "So <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=cos%28theta%29=0.6 ALIGN=MIDDLE  ALT=\"cos%28theta%29=0.6\"   DISABLED_style= \"max-width:90%; height:auto;\" > , and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sin%28theta%29=-0.8 ALIGN=MIDDLE  ALT=\"sin%28theta%29=-0.8\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "From there, you could<BR>\n" );
document.write( "A) calculate <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=tan%28theta%29=sin%28theta%29%2Fcos%28theta%29=-0.8%2F0.6=-4%2F3 ALIGN=MIDDLE  ALT=\"tan%28theta%29=sin%28theta%29%2Fcos%28theta%29=-0.8%2F0.6=-4%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" > ,<BR>\n" );
document.write( "and then apply the trigonometric identity<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=tan%282theta%29=2tan%28theta%29%2F%281-%28tan%28theta%29%29%5E2%29 ALIGN=MIDDLE  ALT=\"tan%282theta%29=2tan%28theta%29%2F%281-%28tan%28theta%29%29%5E2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "So <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=tan%282theta%29=2%28-4%2F3%29%2F%281-%28-4%2F3%29%5E2%29=%28-8%2F3%29%2F%281-16%2F9%29=%28-8%2F3%29%2F%28-7%2F9%29=%288%2F3%29%289%2F7%29=24%2F7 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "B) or calculate <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=cos%282theta%29 ALIGN=MIDDLE  ALT=\"cos%282theta%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sin%282theta%29 ALIGN=MIDDLE  ALT=\"sin%282theta%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > using the trigonometric identities below,<BR>\n" );
document.write( "and then divide sine by cosine to get tangent<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=cos%282theta%29=%28cos%28theta%29%29%5E2-%28sin%28theta%29%29%5E2 ALIGN=MIDDLE  ALT=\"cos%282theta%29=%28cos%28theta%29%29%5E2-%28sin%28theta%29%29%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > and<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sin%282theta%29=2%2Acos%28theta%29%2Asin%28theta%29 ALIGN=MIDDLE  ALT=\"sin%282theta%29=2%2Acos%28theta%29%2Asin%28theta%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );