document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1182118>Question 1182118</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The equation sec x=−0.5 does NOT have a solution because\r<BR>\n" );
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document.write( "it means that cos x = −2 which is outside the range\r<BR>\n" );
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document.write( "of the negative value on the right side\r<BR>\n" );
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document.write( "the equation is not well formulated\r<BR>\n" );
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document.write( "it means that sin x = −2 which is outside the range </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #812102 by </B><A HREF=/tutors/aboutme.mpl?userid=math_tutor2020><B>math_tutor2020(3817)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=math_tutor2020><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=812102\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font color=black size=3><BR>\n" );
document.write( "If sec(x) = -0.5, then cos(x) = -2 if we apply the reciprocal to both sides. Recall that sec = 1/cos.\r<BR>\n" );
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document.write( "Also, recall that the range for cosine is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-1+%3C=+cos%28x%29+%3C=+1 ALIGN=MIDDLE  ALT=\"-1+%3C=+cos%28x%29+%3C=+1\"   DISABLED_style= \"max-width:90%; height:auto;\" >. Meaning that cos(x) between -1 and 1 inclusive of both endpoints. The value -2 is outside this interval, so it's impossible to have cos(x) = -2 where x is a real number. <BR>\n" );
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