document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1189670>Question 1189670</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Solve the following equations for x between 0° and 360°<BR>\n" );
document.write( "a) cosec x = -2<BR>\n" );
document.write( "b) sec x = 5 sin 20°<BR>\n" );
document.write( "c) cot^2 x = 3 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #821121 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=821121\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> a) cosec x = -2\r<BR>\n" );
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document.write( "cosec(x) = 1/sin(x)<BR>\n" );
document.write( "equation becomes:<BR>\n" );
document.write( "1/sin(x) = -2<BR>\n" );
document.write( "solve for sin(x) to get sin(x) = -1/2<BR>\n" );
document.write( "sine is negative in third and fourth quadrant.<BR>\n" );
document.write( "arcsin(1/2) = 30 degrees.<BR>\n" );
document.write( "that's in the first quadrant.<BR>\n" );
document.write( "equivalent angle in the third quadrant is 180 + 30 = 210 degrees.<BR>\n" );
document.write( "equivalent angle in the fourth quadrant is 360 - 30 = 330 degrees.<BR>\n" );
document.write( "x can either be 210 degrees or 330 degrees.<BR>\n" );
document.write( "that's your solution.<BR>\n" );
document.write( "here's what it looks like in a graph.\r<BR>\n" );
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document.write( "b) sec x = 5 sin 20°\r<BR>\n" );
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document.write( "sec(x) = 1/cos(x)<BR>\n" );
document.write( "equation becomes:<BR>\n" );
document.write( "1/cos(x) = 5sin(20)<BR>\n" );
document.write( "solve for cos(x) to get:<BR>\n" );
document.write( "cos(x) = 1/(5sin(20))<BR>\n" );
document.write( "use your calculator to solve for 5sin(20).<BR>\n" );
document.write( "you will get 5sin(20) = 1.710100717.<BR>\n" );
document.write( "cos(x) = 1/that = .58476088.<BR>\n" );
document.write( "solve for x to get:<BR>\n" );
document.write( "x = 54.21390092 degrees.<BR>\n" );
document.write( "that's in the first quadrant.<BR>\n" );
document.write( "cosine is positive in the first and fourth quadrant.<BR>\n" );
document.write( "equivalent angle in the fourth quadrant is 360 - 54.21390092 = 305.7860991 degrees.<BR>\n" );
document.write( "x can be either 54.21390092 and 305.7860991 degrees.<BR>\n" );
document.write( "that's your solution.<BR>\n" );
document.write( "here's what it looks like on a graph.\r<BR>\n" );
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document.write( "c) cot^2 x = 3\r<BR>\n" );
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document.write( "cot^2(x) = 1/tan^2(x)<BR>\n" );
document.write( "equation becomes:<BR>\n" );
document.write( "1/tan^2(x) = 3.<BR>\n" );
document.write( "solve for tan^2(x) to get:<BR>\n" );
document.write( "tan^2(x) = 1/3.<BR>\n" );
document.write( "solve for tan(x) to get:<BR>\n" );
document.write( "tan(x) = sqrt(1/3)<BR>\n" );
document.write( "solve for x to get:<BR>\n" );
document.write( "x = arctan(sqrt(1/3)) = 30 degrees.<BR>\n" );
document.write( "cotangent is positive in the first and third quadrant.<BR>\n" );
document.write( "cotangent is negative in the second and fourth quadrant.<BR>\n" );
document.write( "cotangent^2 is positive in all four quadrants.<BR>\n" );
document.write( "equivalent angle in the second quadrant is 180 - 30 = 150 degrees.<BR>\n" );
document.write( "equivalent angle in the third quadrant is 180 + 30 = 210 degrees.<BR>\n" );
document.write( "equivalent angle in the fourth quadrant is 360 - 30 = 330 degrees.<BR>\n" );
document.write( "x can be either 30, 150, 210, of 340 degrees.<BR>\n" );
document.write( "that's your solution.<BR>\n" );
document.write( "here's what it looks like on a graph.\r<BR>\n" );
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document.write( "let me know if you have any questions.\r<BR>\n" );
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document.write( "theo\r<BR>\n" );
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