document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1142691>Question 1142691</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Find the largest possible domain of y=ln(sin inverse x) \r<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #763398 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=763398\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> the largest domain of y = arcsin(x) appears to be 0 < x <= 1.\r<BR>\n" );
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document.write( "y = sin(x) gives you a value of y = -1 to 1.\r<BR>\n" );
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document.write( "that's the range of y = sin(x).\r<BR>\n" );
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document.write( "y = arcsin(-1) = -90 degrees.<BR>\n" );
document.write( "y = arcsin(1) = 90 degrees.\r<BR>\n" );
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document.write( "the value of x goes from -1 to 1 and the value of y goes from -90 degrees to 90 degrees.\r<BR>\n" );
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document.write( "the domain of y = arcsin(x) is -1 <= x <= 1.\r<BR>\n" );
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document.write( "the domain of y = ln(arcsin(x)) is 0 < x <= 1.\r<BR>\n" );
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document.write( "that's because the natural log of a number requires the number to be greater than 0.\r<BR>\n" );
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document.write( "since arsin(0) = 0, that would be invalid.<BR>\n" );
document.write( "as long as arcsin(x) has x > 0, then the value would be valid.\r<BR>\n" );
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document.write( "i think this is what you are looking for.\r<BR>\n" );
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document.write( "the domain would be 0 <= x <= 1<BR>\n" );
document.write( "the range would be -infinity < y <= ln(90) when working with degrees.<BR>\n" );
document.write( "since 90 degrees * pi / 180 = pi/2 radians, then the range would be -infinity to pi/2 radians when working with radians.\r<BR>\n" );
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document.write( "whether working with degrees or radians, the domain is still 0 < x <= 1.\r<BR>\n" );
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document.write( "the following graphs illustrate this.\r<BR>\n" );
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document.write( "the first 2 graphs show the value of y in degrees.\r<BR>\n" );
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document.write( "the last 2 graphs shosw the value of y in radians.\r<BR>\n" );
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document.write( "in both cases, the value of ln(arcsin(x)) has a domain of 0 < x <= 1.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" src = \"http://theo.x10hosting.com/2019/062801.jpg\" alt=\"$$$\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" src = \"http://theo.x10hosting.com/2019/062802.jpg\" alt=\"$$$\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" src = \"http://theo.x10hosting.com/2019/062803.jpg\" alt=\"$$$\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" src = \"http://theo.x10hosting.com/2019/062804.jpg\" alt=\"$$$\" >\r<BR>\n" );
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document.write( "i'm not exactly sure that this is what you're looking for, but it's what i get based on my interpretation of the problem.\r<BR>\n" );
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