document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1135868>Question 1135868</A>: <I><SPAN STYLE=\"word-break: break-all;\"> it is given that sin A = K, where A is an angle measured in radians,<BR>\n" );
document.write( " and pi < A < (3pi/2)\r<BR>\n" );
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document.write( "If sin B = k, which of the following is the value of B?\r<BR>\n" );
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document.write( "A) A - pi<BR>\n" );
document.write( "B) pi + A<BR>\n" );
document.write( "C) 2pi - A<BR>\n" );
document.write( "D) 3pi - A </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #753604 by </B><A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><B>jim_thompson5910(35256)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><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=753604\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font face=\"times\" color=\"black\" size=\"3\"><BR>\n" );
document.write( "The identities I will be using are<BR>\n" );
document.write( "sin(A+B) = sin(A)cos(B) + cos(A)sin(B)<BR>\n" );
document.write( "and<BR>\n" );
document.write( "sin(A-B) = sin(A)cos(B) - cos(A)sin(B)\r<BR>\n" );
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document.write( "Let's the second identity mentioned to expand out choice A like so<BR>\n" );
document.write( "sin(A - pi) = sin(A)cos(pi) - cos(A)sin(pi)<BR>\n" );
document.write( "sin(A - pi) = sin(A)(-1) - cos(A)(0)<BR>\n" );
document.write( "sin(A - pi) = -sin(A)<BR>\n" );
document.write( "sin(A - pi) = -K<BR>\n" );
document.write( "Choice A is crossed off the list because we want K instead of -K\r<BR>\n" );
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document.write( "Use the first identity to expand out the sine value of choice B<BR>\n" );
document.write( "sin(pi+A) = sin(pi)cos(A) + cos(pi)sin(A)<BR>\n" );
document.write( "sin(pi+A) = (0)cos(A) + (-1)sin(A)<BR>\n" );
document.write( "sin(pi+A) = -sin(A)<BR>\n" );
document.write( "sin(pi+A) = -K<BR>\n" );
document.write( "we run into the same issue we did in choice A. So choice B is crossed off the list as well.\r<BR>\n" );
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document.write( "Go back to the second identity and expand for choice C<BR>\n" );
document.write( "sin(2pi - A) = sin(2pi)cos(A) - cos(2pi)sin(A)<BR>\n" );
document.write( "sin(2pi - A) = (0)cos(A) - (1)sin(A)<BR>\n" );
document.write( "sin(2pi - A) = -sin(A)<BR>\n" );
document.write( "sin(2pi - A) = -K<BR>\n" );
document.write( "Same issue. Cross choice C off the list.\r<BR>\n" );
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document.write( "Repeat for choice D<BR>\n" );
document.write( "sin(3pi - A) = sin(3pi)cos(A) - cos(3pi)sin(A)<BR>\n" );
document.write( "sin(3pi - A) = (0)cos(A) - (-1)sin(A)<BR>\n" );
document.write( "sin(3pi - A) = sin(A)<BR>\n" );
document.write( "sin(3pi - A) = K<BR>\n" );
document.write( "So this proves that sin(B) = K where B = 3pi-A. We have our answer\r<BR>\n" );
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document.write( "Answer: <font color=red size=4>Choice D) 3pi - A</font> <BR>\n" );
document.write( "</font> </SPAN>\n" );
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