document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=901286>Question 901286</A>: <I><SPAN STYLE=\"word-break: break-all;\"> cos alpha= 1/2and tan beta=1/3.find sin(alpha+beta),where alpha and beta are both acute angles\r<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #546645 by </B><A HREF=/tutors/aboutme.mpl?userid=harpazo><B>harpazo(655)</B></A><img src=\"/images/stars/stars-11.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=harpazo><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=harpazo><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=546645\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> We need to find sin alpha and sin beta.\r<BR>\n" );
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document.write( "cosine = adjacent over hypotenuse.\r<BR>\n" );
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document.write( "x^2 + 1^2 = 2^2\r<BR>\n" );
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document.write( "x^2 = 4 - 1\r<BR>\n" );
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document.write( "x^2 = 3\r<BR>\n" );
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document.write( "sqrt{x^2} = sqrt{3)\r<BR>\n" );
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document.write( "x = sqrt{3)\r<BR>\n" );
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document.write( "sin alpha = sqrt{3}/2\r<BR>\n" );
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document.write( "tangent = opposite over adjacent.\r<BR>\n" );
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document.write( "1^2 + 3^2 = x^2\r<BR>\n" );
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document.write( "1 + 9 = x^2\r<BR>\n" );
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document.write( "10 = x^2\r<BR>\n" );
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document.write( "sqrt{10} = sqrt{x^2}\r<BR>\n" );
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document.write( "sqrt{10} = x\r<BR>\n" );
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document.write( "sin beta = 1/sqrt{10}\r<BR>\n" );
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document.write( "We now plug and chug.\r<BR>\n" );
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document.write( "sin(A + B) = sin A cos B + cos A sin B\r<BR>\n" );
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document.write( "Let A = alpha and B = beta for short.\r<BR>\n" );
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document.write( "We have sin alpha and sin beta.\r<BR>\n" );
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document.write( "We need cos beta and cos alpha.\r<BR>\n" );
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document.write( "cos alpha = 1/2 and cos beta = 3/sqrt{10}.\r<BR>\n" );
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document.write( "Plug into formula and simplify.\r<BR>\n" );
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document.write( "Here is the formula you need:\r<BR>\n" );
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document.write( "sin(A + B) = sin A times cos B + cos A times sin B\r<BR>\n" );
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document.write( "Can you finish? \r<BR>\n" );
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document.write( "</TD></TR></TABLE>\n" );