document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=312171>Question 312171</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Please help me with this question and show all steps if possible thank you!<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 #223186 by </B><A HREF=/tutors/aboutme.mpl?userid=nyc_function><B>nyc_function(2741)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=nyc_function><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=nyc_function><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=223186\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> 2sin^2 x - cosx = 0\r<BR>\n" );
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document.write( "One of the Pythagorean Identities is sin^2 x = 1 - cos^2 x.\r<BR>\n" );
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document.write( "Replace your sin^2 x with 1 - cos^2 x.\r<BR>\n" );
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document.write( "2(1 - cos^2 x) - cosx = 0\r<BR>\n" );
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document.write( "We now apply the distributive rule from algebra to remove the parentheses.\r<BR>\n" );
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document.write( "2 - 2cos^2 x - cosx = 0\r<BR>\n" );
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document.write( "Bring everything to the right side of the trig equation and then equate to zero.\r<BR>\n" );
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document.write( "0 = 2cos^2 x + cosx - 2\r<BR>\n" );
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document.write( "To avoid confusion, replace cosx with any letter of choice to complete the factoring process.  Then, at the end, replace the letter your chose with cosx.  More about this later.\r<BR>\n" );
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document.write( "I will use the letter u but you can use any letter.\r<BR>\n" );
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document.write( "2u^2 + u - 2 = 0\r<BR>\n" );
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document.write( "Do you recognize that this is a quadratic equation dressed up as a trig function?\r<BR>\n" );
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document.write( "We now factor like any other quadratic equation.\r<BR>\n" );
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document.write( "To factor, we need to use the quadratic formula from algebra in this case.\r<BR>\n" );
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document.write( "After doing the math on paper, I got two answers for u.\r<BR>\n" );
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document.write( "Here they are:\r<BR>\n" );
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document.write( "u = [-1 + sqrt{17}]/4, which is about 0.781 in decimal form.\r<BR>\n" );
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document.write( "AND\r<BR>\n" );
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document.write( "u = [-1 - sqrt{17}]/4, which is rejected because the value of cosine must lie between 0 and 1. Do you understand why the negative decimal number must be rejected?\r<BR>\n" );
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document.write( "We are working with the positive decimal number. Keep in mind that cosine is positive in the first and fourth quadrants.\r<BR>\n" );
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document.write( "We can now replace u with cosx because we are dealing with trigonometry not algebra.\r<BR>\n" );
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document.write( "We are working with cosx = 0.781.\r<BR>\n" );
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document.write( "Using the inverse cosine key on the calculator, I found the reference angle to be 38 degrees.\r<BR>\n" );
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document.write( "Since we are in quadrants 1 and 4, we now find the values of x in those quadrants.\r<BR>\n" );
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document.write( "In Quadrant 1:\r<BR>\n" );
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document.write( "90 - 38 = 52 degrees\r<BR>\n" );
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document.write( "In Quadrant 4:\r<BR>\n" );
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document.write( "360 - 38 = 322 degrees\r<BR>\n" );
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document.write( "I hope this helps.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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