document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1138070>Question 1138070</A>: <I><SPAN STYLE=\"word-break: break-all;\"> solve 4 cos^2 θ + 2 sin θ = 3 for 0° ≤ θ ≤ 360°  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #755963 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=755963\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> your equation is:\r<BR>\n" );
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document.write( "4 * cos^2(t) + 2 * sin(t) = 3\r<BR>\n" );
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document.write( "since cos^2(t) is equal to 1 - sin^2(t), this equation can be shown as:\r<BR>\n" );
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document.write( "4 * (1 - sin^2(t)) + 2 * sin(t) = 3\r<BR>\n" );
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document.write( "simplify to get:\r<BR>\n" );
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document.write( "4 - 4 * sin^2(t) + 2 * sin(t) = 3\r<BR>\n" );
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document.write( "subtract 3 from both sides of this equation to get:\r<BR>\n" );
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document.write( "-4 * sin^2(t) + 2 * sin(t) + 1 = 0\r<BR>\n" );
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document.write( "let x = sin(t) and this equation becomes:\r<BR>\n" );
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document.write( "-4 * x^2 + 2 * x + 1 = 0\r<BR>\n" );
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document.write( "factor this quadratic equation to get:\r<BR>\n" );
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document.write( "x = 0.80901699437495 or x = -0.30901699437495\r<BR>\n" );
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document.write( "since x = sin(t), this means that sin(t) = 0.80901699437495 or sin(t) = -0.30901699437495\r<BR>\n" );
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document.write( "when sin(t) = 0.80901699437495, your angle is either 54 degrees is 126 degrees.\r<BR>\n" );
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document.write( "when sin(t) = -0.30901699437495, your angle is either 198 degrees or 342 degrees.\r<BR>\n" );
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document.write( "your solution should therefore be either 54, 126, 198, or 342 degrees in the 0 to 360 degree interval.\r<BR>\n" );
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document.write( "you would confirm by evaluating the original equation at each of those angles.\r<BR>\n" );
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document.write( "if you do so, you will see that the original equation is true for all of them.\r<BR>\n" );
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document.write( "therefore, your solution is 54, 126, 198, and 342 degrees in the 0 to 360 degree interval.\r<BR>\n" );
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document.write( "this can be seen graphically as shown below:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" src = \"http://theo.x10hosting.com/2019/040321.jpg\" alt=\"$$$\" >\r<BR>\n" );
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document.write( "in this graph, you set up two equations.\r<BR>\n" );
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document.write( "the first is y = 4 * cos^2(x) + 2 * sin(x)\r<BR>\n" );
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document.write( "the secon is y = 3\r<BR>\n" );
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document.write( "if the first equation is equal to the second equation, the graphs ill intersect and the intersection points will be as shown.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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