document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=136476>Question 136476</A>: <I><SPAN STYLE=\"word-break: break-all;\"> These are very confusing for me.  Here are a couple, I hope to use these examples to help me solve the rest.<BR>\n" );
document.write( "Solve for x,<BR>\n" );
document.write( " a) 4cos^2(2x+90)=3, x is in the interval[0,360)<BR>\n" );
document.write( " b) If cotx=-3, find the Q2 family member of x in degrees<BR>\n" );
document.write( " c) 2sin1/2x=sqrt3 over the interval [0,2pie], keep angle in pie radians<BR>\n" );
document.write( " d) 2cos^2x-sinx-1=0, hint, replace cos^2x with one of the pythagorean identities  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #100016 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=100016\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Solve for x,<BR>\n" );
document.write( "a) 4cos^2(2x+90)=3, x is in the interval[0,360)<BR>\n" );
document.write( "cos^2(2x+90) = 3/4<BR>\n" );
document.write( "cos(2x+90) = +0.75 or -0.75<BR>\n" );
document.write( "If cos(2x+90) = 0.75,<BR>\n" );
document.write( "Take the inverse cosine to get:<BR>\n" );
document.write( "2x+90 = 41.4096 or 2x+90 = -41.4096<BR>\n" );
document.write( "Then x = -24.295 degrees or x = -65.7048 degrees<BR>\n" );
document.write( "----------<BR>\n" );
document.write( "If cos(2x+90) = -0.75<BR>\n" );
document.write( "Take the inverse cosine to get two values in the 2nd and 3rd quadrant<BR>\n" );
document.write( "Then solve for x.<BR>\n" );
document.write( "-------------------------- <BR>\n" );
document.write( "b) If cotx=-3, find the Q2 family member of x in degrees<BR>\n" );
document.write( "If cotx = -3, tanx= (-1/3)<BR>\n" );
document.write( "Take the inverse tan to get:<BR>\n" );
document.write( "x = -18.4349<BR>\n" );
document.write( "The corresponding angle in Q2 is 180-18.4349 = 161.565. degrees<BR>\n" );
document.write( "-------------------<BR>\n" );
document.write( "c) 2sin1/2x=sqrt3 over the interval [0,2pie], keep angle in pie radians<BR>\n" );
document.write( "sin(x/2) = (sqrt3)/2<BR>\n" );
document.write( "Take the inverse sin of (sqrt3)/2 to get:<BR>\n" );
document.write( "x/2 = 1.047197.. radians<BR>\n" );
document.write( "x = 2.094395... radians<BR>\n" );
document.write( "----------------------------<BR>\n" );
document.write( "d) 2cos^2x-sinx-1=0, hint, replace cos^2x with one of the pythagorean identities <BR>\n" );
document.write( "2(1-sin^2x) - sinx -1 = 0<BR>\n" );
document.write( "-2sin^2x  -sinx +1 = 0<BR>\n" );
document.write( "2sin^2x + sinx -1 = 0<BR>\n" );
document.write( "Factor to get:<BR>\n" );
document.write( "(2sinx-1)(sinx+1)=0<BR>\n" );
document.write( "sinx = 1/2 or sinx = -1<BR>\n" );
document.write( "x = 30 or 150 degrees<BR>\n" );
document.write( "x = 270 degrees<BR>\n" );
document.write( "===================<BR>\n" );
document.write( "Cheers,<BR>\n" );
document.write( "Stan H.<BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );