document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=720143>Question 720143</A>: <I><SPAN STYLE=\"word-break: break-all;\"> please help me solve the following trigonometric equation using Pythagorean identity formula:\r<BR>\n" );
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document.write( "1-sin^2theta=0.5 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #441686 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=441686\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> i will use the letter T to represent theta.\r<BR>\n" );
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document.write( "the pythagorean identify is sin^2(T) + cos^2(T) = 1\r<BR>\n" );
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document.write( "subtract sin^2(T) from both sides of this equation to get:\r<BR>\n" );
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document.write( "cos^2(T) = 1 - sin^2(T)\r<BR>\n" );
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document.write( "your equation is 1 - sin^2(T) = .5\r<BR>\n" );
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document.write( "since 1 - sin^2(T) is equivalent to cos^2(T), replace 1 - sin^2(T) with cos^2(T) and you get:\r<BR>\n" );
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document.write( "cos^2(T) = .5\r<BR>\n" );
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document.write( "take the square root of both sides of this equation to get:\r<BR>\n" );
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document.write( "cos(T) = +/- sqrt(.5)\r<BR>\n" );
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document.write( "cos(T) can be + sqrt(.5) or - sqrt(.5)\r<BR>\n" );
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document.write( "if + sqrt(.5), then T is equal to 45 degrees.\r<BR>\n" );
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document.write( "if - sqrt(.5), then T is equal to 135 degrees.\r<BR>\n" );
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document.write( "to find the angle whose cosine is equal to sqrt(.5), you use the cos^-1 function of your calculator.\r<BR>\n" );
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document.write( "the key to solving this, however, is to recognize that:<BR>\n" );
document.write( "1 - sin^2(T) <BR>\n" );
document.write( "is equivalent to cos^2(T) based on the pythagorean formula of:<BR>\n" );
document.write( "sin^2(T) + cost^2(T) = 1.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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