document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=659149>Question 659149</A>: <I><SPAN STYLE=\"word-break: break-all;\"> I think this is trignonmetry i'm not completely sure. Could Someone help me by explaining this and how to answer it. <BR>\n" );
document.write( "(a)Use a trigonometric identity and then algebra to solve the equation sin^2 x = cos x, 0 &#8804; x &#8804; 2&#960;. Give all your solutions in radians. <BR>\n" );
document.write( "(b)On the same set of axes draw the two graphs y = sin^2x and y = cos x for the domain [0,2&#960; ] . Show on your graph where your solutions to part (a) are. </SPAN>\n" );
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document.write( "(a)Use a trigonometric identity and then algebra to solve the equation sin^2 x = cos x, 0 &#8804; x &#8804; 2&#960;. Give all your solutions in radians.<BR>\n" );
document.write( "..<BR>\n" );
document.write( "sin^2x=cosx<BR>\n" );
document.write( "Identity:sin^2x+cos^2x=1<BR>\n" );
document.write( "sin^2x=1-cos^2x<BR>\n" );
document.write( "..<BR>\n" );
document.write( "1-cos^2x=cosx<BR>\n" );
document.write( "cos^2x+cosx-1=0<BR>\n" );
document.write( "let u=cosx<BR>\n" );
document.write( "u^2+u-1=0<BR>\n" );
document.write( "solve for u by following quadratic formula:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=u+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+ ALIGN=MIDDLE  ALT=\"u+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "a=1, b=1, c=-1<BR>\n" );
document.write( "ans<BR>\n" );
document.write( "u&#8776;-1.62 (reject, not in domain)<BR>\n" );
document.write( "or <BR>\n" );
document.write( "u&#8776;.618<BR>\n" );
document.write( "cosx=.618<BR>\n" );
document.write( "from calculator:<BR>\n" );
document.write( "x=.905 and 5.378 radians (in quadrants I and IV where cos>0)<BR>\n" );
document.write( "..<BR>\n" );
document.write( "b)On the same set of axes draw the two graphs y = sin^2x and y = cos x for the domain [0,2&#960; ] . Show on your graph where your solutions to part (a) are.<BR>\n" );
document.write( "..<BR>\n" );
document.write( "I don't have the means to draw graphs for you, but I will provide the coordinates with which you can draw the graphs yourself.<BR>\n" );
document.write( "..<BR>\n" );
document.write( "For cosx for 1 period (0-2&#960;)<BR>\n" );
document.write( "(0,1), (&#960;/2,0), (&#960;,-1), (3&#960;/2,0), (2&#960;,1)<BR>\n" );
document.write( "..<BR>\n" );
document.write( "For sin^2x for 1 period<BR>\n" );
document.write( "(0,0), (&#960;/2,1), (&#960;,0), (3&#960;/2,1), (2&#960;/0)<BR>\n" );
document.write( "..<BR>\n" );
document.write( "If you draw these two curves correctly, you will find that they intersect at coordinates (0.905,0.618) and (5.378,0.618)<BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );