document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1188397>Question 1188397</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Given cos(a) = 1/2, tan(b) = -3/2, 0 < a < ((pi)/2), and ((pi)/2) < b < pi, find sin(a+b), cos(a-b), and tan(a+b)  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #819599 by </B><A HREF=/tutors/aboutme.mpl?userid=Solver92311><B>Solver92311(821)</B></A><img src=\"/images/stars/stars-11.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Solver92311><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=Solver92311><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=819599\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Sunday, April 2, 2017<BR>\n" );
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document.write( "If you know the cosine of an angle and the quadrant where the terminal ray lies, then you can calculate the sine of the angle by:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ \sin\varphi\ =\ \pm\sqrt{1\,-\,\cos^2\varphi}\">\r<BR>\n" );
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document.write( "and then choose the sign using the fact that the sine is positive in QI and QII, and negative in QIII and QIV.\r<BR>\n" );
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document.write( "Once you know the sine and cosine, you can calculate the tangent by using:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ \tan\varphi\ =\ \frac{\sin\varphi}{\cos\varphi}\">\r<BR>\n" );
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document.write( "If you know the tangent of an angle to be <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large \frac{a}{b}\"> and the Quadrant, then you can find both the sine and cosine by:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ \frac{\sin\varphi}{\cos\varphi}\ =\ \frac{a}{b}\">\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ b\sin\varphi\ =\ a\cos\varphi\">\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ b^2\sin^2\varphi\ =\ a^2\cos^2\varphi\">\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ b^2\sin^2\varphi\ =\ a^2(1\ -\ \sin^2\varphi)\">\r<BR>\n" );
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document.write( "And then solve for the sine selecting the sign based on the quadrant.\r<BR>\n" );
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document.write( "Similarly, the cosine can be determined by solving:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ a^2\cos^2\varphi\ =\ b^2(1\ -\ \cos^2\varphi)\">\r<BR>\n" );
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document.write( "and noting that cosine is positive in QI and QIV, negative in QII and QIII.\r<BR>\n" );
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document.write( "The sine, cosine, and tangent of the sum and difference of two angles:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ \sin(a\,\pm\,b)\ =\ \sin(a)\cos(b)\,\pm\,\cos(a)\sin(b)\">\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ \cos(a\,\pm\,b)\ =\ \cos(a)\cos(b)\,\mp\,\sin(a)\sin(b)\">\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ \tan(a\,\pm\,b)\ =\ \frac{\tan(a)\,\pm\,\tan(b)}{1\,\mp\,\tan(a)\tan(b)}\">\r<BR>\n" );
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document.write( "																<BR>\n" );
document.write( "John<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE e^{i\pi}\ +\ 1\ =\ 0\"><BR>\n" );
document.write( "My calculator said it, I believe it, that settles it<BR>\n" );
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document.write( "From <https://www.algebra.com/cgi-bin/upload-illustration.mpl> <BR>\n" );
document.write( "I > Ø<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large \ \\r\"> </SPAN>\n" );
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