document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1040117>Question 1040117</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Need some help drawing and labeling an example of an angle with negative measure in standard position. Then create an angle with a positive measure that is coterminal with this angle. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #655175 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=655175\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> let's say your angle is -90 degrees.<BR>\n" );
document.write( "add 360 to it and the equivalent positive angle is 270 degrees.\r<BR>\n" );
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document.write( "any time you add or subtract 360 degrees from any angle, you get an equivalent angle that is coterminous with that angle.\r<BR>\n" );
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document.write( "if your angle is negative, just keep adding 360 to it until it becomes positive.\r<BR>\n" );
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document.write( "if your angle is positive and you want to get the negative equivalent, just keep subtracting 360 from it until it becomes negative.\r<BR>\n" );
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document.write( "the unit circle is used to demonstrate angles and their equivalents in different quadrants.\r<BR>\n" );
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document.write( "an angle in a different quadrant is equivalent if it has the same values for each of the trigonometric functions.\r<BR>\n" );
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document.write( "for example, using -90 as the angle, it's equivalent positive angle would be 270 degrees.\r<BR>\n" );
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document.write( "the position of 270 degrees in the unit circle is the same position as -90 degrees in the unit circle.\r<BR>\n" );
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document.write( "to get to -90 degrees from 0 degrees, you would rotate the angle clockwise until you reach -90 degrees.\r<BR>\n" );
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document.write( "to get to 270 degrees from 0 degrees, you would rotate the angle counter-clockwise until you reach 270 degrees.\r<BR>\n" );
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document.write( "every time you add 360 degrees to an angle, you are rotating the angle counter-clockwise 360 degrees.\r<BR>\n" );
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document.write( "every time you subtract 360 degrees from an angle, you are rotating the angle clockwise 360 degrees.\r<BR>\n" );
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document.write( "here's a picture of the unit circle.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" src = \"http://theo.x10hosting.com/2016/070801.jpg\" alt=\"$$$\" </>\r<BR>\n" );
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document.write( "the angle used in the example is -90 degrees.<BR>\n" );
document.write( "add 360 to that and you get the equivalent angle of +270 degrees.<BR>\n" );
document.write( "those angles occupy the same position on the unit circle.<BR>\n" );
document.write( "they are equivalent.<BR>\n" );
document.write( "equivalent means the value of all their trig functions is the same.<BR>\n" );
document.write( "you can confirm by using your calculator.\r<BR>\n" );
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document.write( "sin(-90) = -1<BR>\n" );
document.write( "sin(270) = -1\r<BR>\n" );
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document.write( "cos(-90) = 0<BR>\n" );
document.write( "cos(270) = 0\r<BR>\n" );
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document.write( "since tan = sin/cos, if sin is the same and cos is the same, then tan will be the same.\r<BR>\n" );
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document.write( "just to confirm:\r<BR>\n" );
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document.write( "tan(-90) = undefined<BR>\n" );
document.write( "tan(270) = undefined\r<BR>\n" );
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document.write( "similarly, if sin is the same, then csc will be the same because csc is equal to 1/sin.\r<BR>\n" );
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document.write( "similarly, if cos is the same, then sec will be the same because sec is equal to 1/cos.\r<BR>\n" );
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document.write( "just to confirm:\r<BR>\n" );
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document.write( "csc(-90) = -1<BR>\n" );
document.write( "css(270) = -1\r<BR>\n" );
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document.write( "sec(-90) = undefined<BR>\n" );
document.write( "sec(270) = undefined\r<BR>\n" );
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document.write( "a value of undefined is caused by a division by 0.\r<BR>\n" );
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document.write( "what this says is that you only really need to check sine or cosine.<BR>\n" );
document.write( "if they are the same, then the rest of the trig functions will be the same because those functions are derived from sine and cosine.\r<BR>\n" );
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document.write( "tan = sin/cos<BR>\n" );
document.write( "cot = cos/sin<BR>\n" );
document.write( "csc = 1/sin<BR>\n" );
document.write( "sec = 1/cos\r<BR>\n" );
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document.write( " </SPAN>\n" );
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