document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=964616>Question 964616</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Find sin^-1 x for the given x. Express your answer as a rational multiple of pi. ranging from pi/2 to 3pi/2. sin^-1 0.5=? how do you solving these kind of problems???  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #589446 by </B><A HREF=/tutors/aboutme.mpl?userid=rothauserc><B>rothauserc(4718)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=rothauserc><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=rothauserc><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=589446\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> sin^-1 0.5 = ?<BR>\n" );
document.write( "This problem is asking you to calculate the inverse sign function for 0.5, the answer can be in degrees or radians.  If your teacher allows you to use a calculator, then look for the sin^-1 function.  Sometimes the calculator will have an inverse function that applies to trig functions.<BR>\n" );
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document.write( "sin^-1 0.5 = 30 degrees, which implies that sin 30 = 0.5<BR>\n" );
document.write( "note that 30 degrees is not the only answer, since trig functions have a period of 360 degrees.<BR>\n" );
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document.write( "We are asked to evaluate sin^-1 0.5 over pi/2 to 3pi/2.  Note that pi is 180 degrees for trig functions, therefore<BR>\n" );
document.write( "we evaluate sin^-1 0.5 from 90 degrees to 270 degrees<BR>\n" );
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document.write( "sin 150 = 0.5, <BR>\n" );
document.write( "note sin 210 = -0.5<BR>\n" );
document.write( "therefore between 90 degrees and 270 degrees, we have one answer sin 150 = 0.5<BR>\n" );
document.write( "now we need to convert 150 to a rational multiple of pi (180)<BR>\n" );
document.write( "150 / 180 = 5pi / 6<BR>\n" );
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document.write( "consider the graph of the sin function<BR>\n" );
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document.write( "The minimum of the first dip below the x-axis corresponds to 270 degrees and the first maximum above the x-axis corresponds to 90 degrees.  Now the values on the y-axis range over +1 to -1, so if you draw a line (green line) parallel to the x-axis half way between 0 and 1 (0.5), you see that there is just one positive value between 90 and 270 degrees. \r<BR>\n" );
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