document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=341395>Question 341395</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Find the exact value of cos (-420 degrees)<BR>\n" );
document.write( "a. -1/2<BR>\n" );
document.write( "b. 1/2<BR>\n" );
document.write( "c. sqrt3/2<BR>\n" );
document.write( "d. -sqrt3/2 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #244479 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=244479\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The exact value of cosine -420 degrees is 1/2.\r<BR>\n" );
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document.write( "You can find it using your calculator.\r<BR>\n" );
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document.write( "Put in -420 and hit cosine button and you will see that the answer is .5\r<BR>\n" );
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document.write( "The hard way to find it is to get the equivalent angle that is less than 360 degrees.\r<BR>\n" );
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document.write( "Add 360 to -420 and you get -60 degrees.\r<BR>\n" );
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document.write( "-60 degrees is in the fourth quadrant.\r<BR>\n" );
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document.write( "In the fourth quadrant, the cosine is positive.\r<BR>\n" );
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document.write( "The cosine of 60 degrees is the adjacent side divided by the hypotenuse.\r<BR>\n" );
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document.write( "The adjacent side of a 60 degree triangle in the fourth quadrant is positive.\r<BR>\n" );
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document.write( "The hypotenuse of any right triangle formed by any angle angle is always positive, regardless of what quadrant the angle is in.\r<BR>\n" );
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document.write( "The cosine of -60 degrees is 1/2 and is positive.\r<BR>\n" );
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document.write( "The cosine of -60 degrees is the same as the cosine of a 60 degree angle that resides in the fourth quadrant.\r<BR>\n" );
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document.write( "In the following diagram, you should be able to see that better.\r<BR>\n" );
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document.write( "The triangle is ABC.\r<BR>\n" );
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document.write( "AB is the side adjacent to to the 60 degree angle.\r<BR>\n" );
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document.write( "The 60 degree angle is in the fourth quadrant, and is there equal to an angle of -60 degrees because it is 60 degrees below the 0 degree line.\r<BR>\n" );
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document.write( "AC is the hypotenuse of the right triangle formed by AB, BC, and AC.\r<BR>\n" );
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document.write( "the angle between AB and BC is a right angle.\r<BR>\n" );
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document.write( "The x-axis to the right of A is the 0 degree line.<BR>\n" );
document.write( "The y-axis above A is the 90 degree line.<BR>\n" );
document.write( "The x-axis to the left of A is the 180 degree line.<BR>\n" );
document.write( "The y-axis below A is the 270 degree line.\r<BR>\n" );
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document.write( "that's for positive angles.\r<BR>\n" );
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document.write( "For negative angle, the following holds:\r<BR>\n" );
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document.write( "The x-axis to the right of A is the -360 degree line.<BR>\n" );
document.write( "The y-axis above A is the -270 degree line.<BR>\n" );
document.write( "The x-axis to the left of A is the -180 degree line.<BR>\n" );
document.write( "The y-axis below A is the -90 degree line.\r<BR>\n" );
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document.write( "the x-axis to the right of A is also the 360 degree line.\r<BR>\n" );
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document.write( "That's because one complete rotation through the circle is equal to 360 degrees.\r<BR>\n" );
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