document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=790340>Question 790340</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Explain why Sine (theta + pi/2) = Cosine(theta) and why Cosine (theta + pi/2) = -Sine(theta) </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #479750 by </B><A HREF=/tutors/aboutme.mpl?userid=lwsshak3><B>lwsshak3(11628)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=lwsshak3><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=479750\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Explain why Sine (theta + pi/2) = Cosine(theta) and why Cosine (theta + pi/2) = -Sine(theta)<BR>\n" );
document.write( "***<BR>\n" );
document.write( "sin(x+&#960;/2)=cos(x)<BR>\n" );
document.write( "cos(x+&#960;/2)=-sin(x)<BR>\n" );
document.write( "..<BR>\n" );
document.write( "Adding &#960;/2 moves the reference angle one quadrant over and changes the reference angle to the complement of the original angle. So, cos of the complement=sin of the angle. Also, the sign changes when moving the sin but the sign does not change when moving the cos. Four examples follow using degrees: (special angles for used for ease of explaning, but should work for any angles)<BR>\n" );
document.write( "..<BR>\n" );
document.write( "let x=30 deg in quadrant I<BR>\n" );
document.write( "reference angle=30 deg<BR>\n" );
document.write( "30+90=120 deg in quadrant II<BR>\n" );
document.write( "reference angle=60 deg<BR>\n" );
document.write( "sin 30=1/2<BR>\n" );
document.write( "cos 120=-1/2<BR>\n" );
document.write( "-cos(x+90)=sin(x)<BR>\n" );
document.write( "cos(x+90)=-sin(x)<BR>\n" );
document.write( "..<BR>\n" );
document.write( "let x=60 deg in quadrant I<BR>\n" );
document.write( "reference angle=60 deg<BR>\n" );
document.write( "60+90=150 deg in quadrant II<BR>\n" );
document.write( "reference angle=30 deg<BR>\n" );
document.write( "cos 60=1/2<BR>\n" );
document.write( "sin 150=1/2<BR>\n" );
document.write( "sin(x+90)=cos(x)<BR>\n" );
document.write( "..<BR>\n" );
document.write( "let x=120 deg in quadrant II<BR>\n" );
document.write( "reference angle=30 deg<BR>\n" );
document.write( "120+90=210 deg in quadrant III<BR>\n" );
document.write( "reference angle=60 deg<BR>\n" );
document.write( "cos 120=-1/2<BR>\n" );
document.write( "sin 210=-1/2<BR>\n" );
document.write( "sin(x+90)=cos(x)\r<BR>\n" );
document.write( "\n" );
document.write( "..<BR>\n" );
document.write( "let x=330 deg in quadrant IV<BR>\n" );
document.write( "reference angle=30 deg<BR>\n" );
document.write( "330+90=420 deg in quadrant I<BR>\n" );
document.write( "reference angle=60 deg<BR>\n" );
document.write( "sin 330=-1/2<BR>\n" );
document.write( "cos 420=1/2<BR>\n" );
document.write( "cos(x+90)=-sin(x)\r<BR>\n" );
document.write( "\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );