document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=522806>Question 522806</A>: <I><SPAN STYLE=\"word-break: break-all;\"> If x is measured in radians, then the derivative of Sin[x] with respect to x is Cos[x].\r<BR>\n" );
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document.write( "Use the formula Sin [x degrees] = Sin [2&#960;/360 x radians]<BR>\n" );
document.write( "to calculate the derivative of Sin [x degrees] with respect to x.\r<BR>\n" );
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document.write( "Why does the resulting formula make calculus difficult if you insist on working with degrees instead of radians?\r<BR>\n" );
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document.write( "Thanks for any help you can offer! </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #347023 by </B><A HREF=/tutors/aboutme.mpl?userid=Alan3354><B>Alan3354(69443)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Alan3354><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=Alan3354><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=347023\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> If x is measured in radians, then the derivative of Sin[x] with respect to x is Cos[x].\r<BR>\n" );
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document.write( "Use the formula Sin [x degrees] = Sin [2&#960;/360 x radians]<BR>\n" );
document.write( "to calculate the derivative of Sin [x degrees] with respect to x.<BR>\n" );
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document.write( "f(x) = sin(x), x in degrees<BR>\n" );
document.write( "f(x) = sin(x*180/pi) radians<BR>\n" );
document.write( "f'(x) = cos(x*180/pi)*(180/pi), x in degrees<BR>\n" );
document.write( "f'(x) = (180/pi)*cos(x), x in radians<BR>\n" );
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document.write( "Why does the resulting formula make calculus difficult if you insist on working with degrees instead of radians?<BR>\n" );
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document.write( "It's more complicated because x is multiplied by a constant, (180/pi).<BR>\n" );
document.write( "Degrees are \"artificial\" or arbitrary units, the same as gradients.<BR>\n" );
document.write( "Radians are a function of the ratio of the arc length to the radius, so the units of the circle, cm, feet, miles, whatever, are canceled. Radians are \"unitless\" measure.<BR>\n" );
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