document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1186660>Question 1186660</A>: <I><SPAN STYLE=\"word-break: break-all;\"> For the following trigonometric function, identify whether the identity stated is true or false. If it is true, demonstrate this with a diagram on the unit circle. if it is false, identify what the expression on the left actually is : <BR>\n" );
document.write( "Cos(3pi/2 + x) = sin(x) </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #817611 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=817611\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> the identity you are looking for is:\r<BR>\n" );
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document.write( "cos(a + b) = cos(a) * cos(b) - sin(a) * sin(b)\r<BR>\n" );
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document.write( "your problem states that:\r<BR>\n" );
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document.write( "cos(3pi/2 + x) = sin(x)\r<BR>\n" );
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document.write( "if you let a = 3pi/2 and b = x, then your identity equation of:\r<BR>\n" );
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document.write( "cos(a + b) = cos(a) * cos(b) - sin(a) * sin(b) becomes:\r<BR>\n" );
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document.write( "cos(3pi/2 + x) = cos(3pi/2) * cos(x) - sin(3pi/2) * sin(x).\r<BR>\n" );
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document.write( "you can use your calculator to find::\r<BR>\n" );
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document.write( "cos(3pi/2) = 0\r<BR>\n" );
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document.write( "sin(3pi/2) = -1\r<BR>\n" );
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document.write( "make sure you set your calculator to radians when you do this.\r<BR>\n" );
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document.write( "if you are not comfortable working with radians, then convert 3pi/2 radians to degrees by multiplying it by 180 / pi.\r<BR>\n" );
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document.write( "3pi/2 * 180/pi = 3/2 * 180 = 270 degrees.\r<BR>\n" );
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document.write( "set your calculator to degrees and you will find that:\r<BR>\n" );
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document.write( "cos(270) = 0\r<BR>\n" );
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document.write( "sin(270) = -1\r<BR>\n" );
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document.write( "these are the same value when the angle is in degrees and when the angle is in radians.\r<BR>\n" );
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document.write( "the conversion factor is:\r<BR>\n" );
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document.write( "degrees = radians * 180 / pi.\r<BR>\n" );
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document.write( "radians = degrees * pi / 180.\r<BR>\n" );
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document.write( "in your identity equation of:\r<BR>\n" );
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document.write( "cos(3pi/2 + x) = cos(3pi/2) * cos(x) - sin(3pi/2) * sin(x).\r<BR>\n" );
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document.write( "replace cos(3pi/2) with 0 and replace sin(3pi/2) with -1 to get:\r<BR>\n" );
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document.write( "cos(3pi/2 + x) = 0 * cos(x) - (-1 * sin(x).\r<BR>\n" );
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document.write( "simplify to get:\r<BR>\n" );
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document.write( "cos(3pi/2 + x) = 0 + 1 * sin(x).\r<BR>\n" );
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document.write( "simplify further to get:\r<BR>\n" );
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document.write( "cos(3pi/2 + x) = sin(x)\r<BR>\n" );
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document.write( "this confirms the identity is good.\r<BR>\n" );
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document.write( "you can demonstrate this is true on the unit circle by showing an example:\r<BR>\n" );
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document.write( "x = 30 degrees.\r<BR>\n" );
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document.write( "270 + x = 300 degrees.\r<BR>\n" );
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document.write( "the reference angle for 300 degrees is equal to 360 - 300 = 60 degrees.\r<BR>\n" );
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document.write( "here's what it looks like on the unit circle graph.\r<BR>\n" );
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document.write( "the 300 degree angle is equal to 270 + 30.\r<BR>\n" );
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document.write( "the 300 degree angle is also equal to 360 - 60.\r<BR>\n" );
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document.write( "the 300 degree angle forms the triangle ABD.\r<BR>\n" );
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document.write( "the reference angle for the 300 degree angle is equal to 60 degrees.\r<BR>\n" );
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document.write( "that's angle DAB in the diagram.\r<BR>\n" );
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document.write( "cos(300) is equal to adjadcent side divided by hypotenuse.\r<BR>\n" );
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document.write( "hypotenuse is equal to 1.<BR>\n" );
document.write( "adjacent side is AD = .5<BR>\n" );
document.write( "cos(300) is therefore equal to .5/1 = .5.\r<BR>\n" );
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document.write( "sin(30) is equal to .5 as well.\r<BR>\n" );
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document.write( "therefore, if x = 30 degrees, then cos(270 + 30) = sin(30).\r<BR>\n" );
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document.write( "that's because 270 + 30 = 300 and you get:\r<BR>\n" );
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document.write( "cos(300) = sin(30).\r<BR>\n" );
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document.write( " </SPAN>\n" );
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