document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=170144>Question 170144</A>: <I><SPAN STYLE=\"word-break: break-all;\"> I'm attempting to do corrections on a test, but these three questions are giving me trouble! I've tried several different things, and I keep coming up with the same (wrong!) answer!\r<BR>\n" );
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document.write( "1) If <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x ALIGN=MIDDLE  ALT=\"x\"   DISABLED_style= \"max-width:90%; height:auto;\" > is an angle in quadrant 4 and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=Cot%28x%29=+-7%2F24 ALIGN=MIDDLE  ALT=\"Cot%28x%29=+-7%2F24\"   DISABLED_style= \"max-width:90%; height:auto;\" >, find the value of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=Sin ALIGN=MIDDLE  ALT=\"Sin\"   DISABLED_style= \"max-width:90%; height:auto;\" ><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2F2 ALIGN=MIDDLE  ALT=\"1%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x ALIGN=MIDDLE  ALT=\"x\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "2) What is the solution set of the equation\r<BR>\n" );
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document.write( " <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=Sin%282x%29+-+Cos%5E2x%2B1+ ALIGN=MIDDLE  ALT=\"Sin%282x%29+-+Cos%5E2x%2B1+\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+Sin%5E2x%2B+Sin%28x%29+ ALIGN=MIDDLE  ALT=\"+Sin%5E2x%2B+Sin%28x%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" > in the interval <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0%3C=x%3C2pi ALIGN=MIDDLE  ALT=\"0%3C=x%3C2pi\"   DISABLED_style= \"max-width:90%; height:auto;\" >?\r<BR>\n" );
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document.write( "3) Find the solution set of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=6Sin%28x%29+%2B+11=+2Csc%28x%29 ALIGN=MIDDLE  ALT=\"6Sin%28x%29+%2B+11=+2Csc%28x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > over the domain <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0%3Cx%3C360 ALIGN=MIDDLE  ALT=\"0%3Cx%3C360\"   DISABLED_style= \"max-width:90%; height:auto;\" >°.<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 #125583 by </B><A HREF=/tutors/aboutme.mpl?userid=stanbon><B>stanbon(75887)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=stanbon><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/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=125583\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> 1) If x is an angle in quadrant 4 and cotx= -7/24, find the value of <BR>\n" );
document.write( "sin[(1/2)x].<BR>\n" );
document.write( "If cotx = -7/24, x = 7 and y = -24<BR>\n" );
document.write( "Then r = sqrt(7^2 + 24^2) = 25<BR>\n" );
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document.write( "sin[(1/2)x] = sqrt[(1-cos(x))/2]<BR>\n" );
document.write( "So, sin[(1/2)x] = sqrt[(1-(7/25))/2] = sqrt[9/25] = 3/5<BR>\n" );
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document.write( "2) What is the solution set of the equation sin(2x)-cos^2(x+1) = sin^2(x)+sinx  in the interval 0<x<2pi?<BR>\n" );
document.write( "Comment: That is a mess to analyze.  Graph the left side and the right side<BR>\n" );
document.write( "separagely and see where they intersect under the condition the 0<x<2pi.<BR>\n" );
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document.write( "3) Find the solution set of 6sinx + 11= 2cscx over the domain 0<x<360.<BR>\n" );
document.write( "Multiply thru by sin(x) to get:<BR>\n" );
document.write( "6sin^2(x) + 11sin(x) - 2 = 0<BR>\n" );
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document.write( "Let w = sin(x)<BR>\n" );
document.write( "Substitute to get:<BR>\n" );
document.write( "6w^2 + 11w - 2 = 0<BR>\n" );
document.write( "6w^2 +12w - w -2= 0<BR>\n" );
document.write( "6w(w+2) -(w+2) = 0<BR>\n" );
document.write( "(w+2)(6w-1) = 0<BR>\n" );
document.write( "w = -2 or w = 1/6<BR>\n" );
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document.write( "Solve for x:<BR>\n" );
document.write( "sin(x) = -2 or sin(x)= 1/6<BR>\n" );
document.write( "sin(x) cannot be -2.<BR>\n" );
document.write( "If sin(x) = 1/6, x = 9.594.. degrees or 170.41 degrees<BR>\n" );
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document.write( "Cheers,<BR>\n" );
document.write( "Stan H.\r<BR>\n" );
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