document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=839654>Question 839654</A>: <I><SPAN STYLE=\"word-break: break-all;\"> sin(x)=1/3, find cos(x) </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #505790 by </B><A HREF=/tutors/aboutme.mpl?userid=Theo><B>Theo(13342)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Theo><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=Theo><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=505790\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> sin(x) = 1/3<BR>\n" );
document.write( "cos(x) = sqrt(8)/3\r<BR>\n" );
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document.write( "not sure how you're supposed to find this, but one way is to use the trigonometric identity of  sin^2(x) + cos^2(x) = 1.\r<BR>\n" );
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document.write( "this becomes (1/3)^2 + cos^2(x) = 1.<BR>\n" );
document.write( "subtract (1/3)^2 from both sides of this equation to get:<BR>\n" );
document.write( "cos^2(x) = 1 - (1/3)^2<BR>\n" );
document.write( "simplify to get:<BR>\n" );
document.write( "cos^2(x) = 1 - 1/9 which then becomes:<BR>\n" );
document.write( "cos^2(x) = 9/9 - 1/9 which then becomes:<BR>\n" );
document.write( "cos^2(x) = 8/9).<BR>\n" );
document.write( "take the square root of both sides of this equation to get:<BR>\n" );
document.write( "cos(x) = sqrt(8)/3.\r<BR>\n" );
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document.write( "you can also find it by using the right triangle as your guide.<BR>\n" );
document.write( "let your right triangle be ABC with the right angle at C.\r<BR>\n" );
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document.write( "a diagram of your triangle is shown below:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" src = \"http://theo.x10hosting.com/2014/feb101.jpg\" alt = \"$$$\" < />\r<BR>\n" );
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document.write( "in this diagram, you can see that side a is opposite angle A and side b is opposite angle B and side c is opposite angle C.\r<BR>\n" );
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document.write( "sine (A) = opposite / hypotenuse = a/c = 1/3.<BR>\n" );
document.write( "this means that a is equal to 1 and c is equal 3.\r<BR>\n" );
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document.write( "since this is a right triangle, a^2 + b^2 = c^2 which translates to:<BR>\n" );
document.write( "1^2 + b^2 = 3^2 which simplifies to:<BR>\n" );
document.write( "1 + b^2 = 9<BR>\n" );
document.write( "subtract 1 from both sides of this triangle to get:<BR>\n" );
document.write( "b^2 = 8 which makes:<BR>\n" );
document.write( "b = sqrt(8).\r<BR>\n" );
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document.write( "cosine (A) = adjacent / hypotenuse = b/c = sqrt(8) / 3.\r<BR>\n" );
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document.write( "you get the same answer either way.\r<BR>\n" );
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