document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=552469>Question 552469</A>: <I><SPAN STYLE=\"word-break: break-all;\"> determine the period of y = tan 2x </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #360393 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=360393\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> first you have to find the period for y = tan(x)<BR>\n" );
document.write( "that is not 360 degrees as you might suppose.<BR>\n" );
document.write( "tan x repeats every 180 degrees.<BR>\n" );
document.write( "it's normal period is therefore 180 degrees.<BR>\n" );
document.write( "the period is determined by the normal period divided by the frequency.<BR>\n" );
document.write( "that would make tan(2x) period equal to 180/2 = 90 degrees.<BR>\n" );
document.write( "below is a graph of tan(x)<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph%28600%2C600%2C0%2C2%2Api%2C-5%2C5%2Ctan%28x%29%2C100%28x-pi%2F2%29%2C100%28x-3pi%2F2%29%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "those vertical lines are at 90 degrees (pi/2) and 270 degrees (3pi/2)<BR>\n" );
document.write( "that's a period of 180 degrees (pi).<BR>\n" );
document.write( "below is a graph of tan(2x)<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph%28600%2C600%2C0%2C2%2Api%2C-5%2C5%2Ctan%282x%29%2C100%28x-pi%2F4%29%2C100%28x-3pi%2F4%29%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "those vertical lines are now at 45 degrees (pi/4) and 135 degrees (3pi/4)<BR>\n" );
document.write( "that's a period of 90 degrees (2pi/4 or pi/2)<BR>\n" );
document.write( "the frequency was doubled (2x instead of x).<BR>\n" );
document.write( "the period was halved (90 degrees instead of 180 degrees).<BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );