document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=767520>Question 767520</A>: <I><SPAN STYLE=\"word-break: break-all;\"> This is a 3-part question.  <BR>\n" );
document.write( "1) Solve the following equation.  Which of its values from the interval 0-180 degrees are correct? sin^2a + 1.5sina = 1<BR>\n" );
document.write( "   a) 30 degrees, 150 degrees; b) 45 degrees, 120 degrees; c) 60 degrees, 150 degrees; d) 30 degrees, 110 degrees.<BR>\n" );
document.write( "2) Why can't we use the solution sina = -2 of the equation?<BR>\n" );
document.write( "3) Solve also the equation sin^2a - 1.5sina = 1.\r<BR>\n" );
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document.write( "I do not know how to even begin to solve this problem.  If you are unable to help me, could you recommend where I might look for help as I cannot find anything about it on the Internet. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #467703 by </B><A HREF=/tutors/aboutme.mpl?userid=solver91311><B>solver91311(24713)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=solver91311><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=solver91311><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=467703\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font face=\"Times New Roman\" size=\"+2\">\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ \sin^2(a)\ +\ 1.5\sin(a)\ =\ 1\">\r<BR>\n" );
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document.write( "Let <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE u\ =\ \sin(a)\">, then\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ u^2\ +\ 1.5u\ -\ 1\ =\ 0\">\r<BR>\n" );
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document.write( "Solve the quadratic, which factors:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ \left(u\ +\ 2\right)\left(u\ -\ \frac{1}{2}\right)\ =\ 0\">\r<BR>\n" );
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document.write( "Then substitute back, so \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ \sin(a)\ =\ -2\">\r<BR>\n" );
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document.write( "or\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ \sin(a)\ =\ \frac{1}{2}\">\r<BR>\n" );
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document.write( "Discard the <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE -2\"> root because the range of the <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE y\ =\ \sin\varphi\"> function is <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \left\{y\ \in\ \mathbb{R}\ |\ -1\ \leq\ y\ \leq\ 1\right\}\">\r<BR>\n" );
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document.write( "Using the unit circle:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" src=\"http://upload.wikimedia.org/wikipedia/commons/4/4c/Unit_circle_angles_color.svg\">\r<BR>\n" );
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document.write( "The value of <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \sin\"> for an angle is the <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE y\">-coordinate of the point of intersection of the terminal ray of the angle and the unit circle.  So find the two points in the desired interval where the <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE y\">-coordinate equals <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \frac{1}{2}\">\r<BR>\n" );
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document.write( "Solve your other problem the same way, but you might want to reconsider the interval for your solutions if you are going to have any solutions at all.\r<BR>\n" );
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document.write( "John<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE e^{i\pi}\ +\ 1\ =\ 0\"><BR>\n" );
document.write( "My calculator said it, I believe it, that settles it<BR>\n" );
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