document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1183085>Question 1183085</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Sketch sinx and its inverse on the same set of axes for 0≤ x ≤ (pi/2)\r<BR>\n" );
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document.write( "I sketched sinx but I don't know how to sketch it's inverse on the same axis, as for its inverse I know that when x = 1, y = (pi/2) but I already put the radians unit on the x axis. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #813244 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=813244\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> putting them on the same axis is tricky, but it can be done.\r<BR>\n" );
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document.write( "we'll work in radians.\r<BR>\n" );
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document.write( "the graph of y = sin(x) is shown below.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" src = \"http://theo.x10hosting.com/2021/071805.jpg\" >\r<BR>\n" );
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document.write( "the graph of y = sin^-1(x) is shown below:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" src = \"http://theo.x10hosting.com/2021/071806.jpg\" >\r<BR>\n" );
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document.write( "the difficulty is that:\r<BR>\n" );
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document.write( "when you graph y = sin(x), x is the angle and y is the trig function value.\r<BR>\n" );
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document.write( "when you graph y = sin^-1(x), x is the trig function value and y is the angle.\r<BR>\n" );
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document.write( "to graph them on the same axes, let the x-axis remain as the angle.\r<BR>\n" );
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document.write( "the functions are y = sin(x) and y = sin^-1(sin(x)).\r<BR>\n" );
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document.write( "that graph looks like this:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" src = \"http://theo.x10hosting.com/2021/071807.jpg\" >\r<BR>\n" );
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document.write( "the blue graph is y = sin(x).<BR>\n" );
document.write( "the red graph is y = sin^-1(x).\r<BR>\n" );
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document.write( "when x = pi/2, y = sin(x) = 1 and y = sin^-1(sin(x)) = pi/2, as shown on the graph.\r<BR>\n" );
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document.write( "the coordinate point for y = sin^-1) is shown as (pi/2,pi/2)<BR>\n" );
document.write( "that means the x-value is pi/2 and the y-value is pi/2).<BR>\n" );
document.write( "the x-value is pi/2, which is the angle.\r<BR>\n" );
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document.write( "y = sin(x) is equal to 1.<BR>\n" );
document.write( "the coordinate points are (pi/2,1)<BR>\n" );
document.write( "this is what is shown on the blue graph.\r<BR>\n" );
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document.write( "y = sin^-1(sin(x)) is equal to sin^-1(1) which is equal to pi/2.<BR>\n" );
document.write( "the coordinate points are (pi/2,pi/2)<BR>\n" );
document.write( "this is what is shown on the red graph.\r<BR>\n" );
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document.write( "keep in mind that the function y = sin^-1(sin(x)) will always make the value of y equal to the value of x.\r<BR>\n" );
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document.write( "not matter what value of x you choose, y will always be equal to x.\r<BR>\n" );
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document.write( "for example, if x = pi/4, sin(pi/4) = .7071067812.\r<BR>\n" );
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document.write( "sin^-1(.7071067812) = .7853981634.<BR>\n" );
document.write( "divide that by pi and it becomes .25 * pi which is the same as pi/4.\r<BR>\n" );
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document.write( "sin-1(sin(pi/4) is equal to pi/4.\r<BR>\n" );
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document.write( "sin^-1(sin(pi/2) is equal to pi/2 as shown on the graph.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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