document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1197163>Question 1197163</A>: <I><SPAN STYLE=\"word-break: break-all;\"> If −𝜋 ≤ 𝑥 ≤ 0, then cos−1(cos 𝑥) is:<BR>\n" );
document.write( "A)𝑥 B)𝜋−𝑥 C)2𝜋+𝑥 D)2𝜋−𝑥 E)None </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #830300 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=830300\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> if you graph the equation, you can see what's going on.<BR>\n" );
document.write( "the graph is shown below:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" src = \"http://theo.x10hosting.com/2022/101203.jpg\"><BR>\n" );
document.write( "you can see from the graph that when x = pi/2, y = arccos(cos(x)) = arccos(cos(pi/2)) = pi/2.<BR>\n" );
document.write( "that would indicate that arccos(cos(x)) = x.<BR>\n" );
document.write( "that's true when 0 < x < pi.<BR>\n" );
document.write( "arccos(cos(-pi/2)) = pi/2 as well.<BR>\n" );
document.write( "however, since the angle is -pi/2, then the coordinate pair is (-pi/2,pi/2) which indicates that arccos(x) = -x when -pi < x < 0<BR>\n" );
document.write( "the equivalent positive angle of -x is equal to -pi/2 + 2pi = 3pi/2.<BR>\n" );
document.write( "that would be 2pi + x because 2pi + (-pi/2) = 3pi/2.<BR>\n" );
document.write( "this is very tough to see unless you can graph it.<BR>\n" );
document.write( "the graphing software i used is at <a  rel=nofollow HREF= \"https://www.desmos.com/calculator\" target = \"_blank\">https://www.desmos.com/calculator</a><BR>\n" );
document.write( "it looks to me that your solution is selection C which is 2pi + x.\r<BR>\n" );
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document.write( "you didn't have -x as a solution.<BR>\n" );
document.write( "you needed to now that -x was equivalent to 2pi - (-x) = 2pi + x.<BR>\n" );
document.write( "arccos(cos(-pi/2) = pi/2.<BR>\n" );
document.write( "arccos(cos(2pi+pi/2) = pi/2.\r<BR>\n" );
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document.write( "let me know if you have any questions.<BR>\n" );
document.write( "theo </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );