document.write( "Question 170144: I'm attempting to do corrections on a test, but these three questions are giving me trouble! I've tried several different things, and I keep coming up with the same (wrong!) answer!\r
\n" ); document.write( "\n" ); document.write( "1) If $\"x\"$ is an angle in quadrant 4 and $\"Cot%28x%29=+-7%2F24\"$ , find the value of $\"Sin\"$ $\"1%2F2\"$ $\"x\"$ .\r
\n" ); document.write( "\n" ); document.write( "2) What is the solution set of the equation\r
\n" ); document.write( "\n" ); document.write( " $\"Sin%282x%29+-+Cos%5E2x%2B1+\"$ = $\"+Sin%5E2x%2B+Sin%28x%29+\"$ in the interval $\"0%3C=x%3C2pi\"$ ?\r
\n" ); document.write( "\n" ); document.write( "3) Find the solution set of $\"6Sin%28x%29+%2B+11=+2Csc%28x%29\"$ over the domain $\"0%3Cx%3C360\"$ °.
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Algebra.Com's Answer #125607 by Edwin McCravy(20060) $\"\"$ $\"About$

You can put this solution on YOUR website!
Stanbon's solution is correct but he does not do problem 2 and he does not explain why we know to take the positive square root in 1.\r
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document.write( "1) If  is an angle in quadrant 4 and , find the value of .\r\n" );
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document.write( "Since this involves drawing a graph in which  represents\r\n" );
document.write( "the horizontal axis, not an angle,  I will temporarily change\r\n" );
document.write( " to  to avoid a conflict of letters.  Change\r\n" );
document.write( "the problem to read this way:\r\n" );
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document.write( "1) If  is an angle in quadrant 4 and , find the value of .\r\n" );
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document.write( "We must use the identity:\r\n" );
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document.write( "However we do not know \r\n" );
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document.write( "So we must first draw the picture of the angle :\r\n" );
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document.write( "We know that  is by definition , we\r\n" );
document.write( "can draw the angle in the 4th quadrant with referent angle\r\n" );
document.write( "is inside a triangle whose horizontal side  is taken\r\n" );
document.write( "to be the numerator of , considered positive because\r\n" );
document.write( "it goes right of the y-axis, and whose vertical side  is taken as \r\n" );
document.write( "the denominator , taken negative because it goes down\r\n" );
document.write( "below the x-axis: \r\n" );
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document.write( "Next we calculate  by the Pythagorean theorem:\r\n" );
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document.write( "So we label the slanted line segment . \r\n" );
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document.write( "Now we can find \r\n" );
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document.write( "So we substitute  for  in\r\n" );
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document.write( "Next we must decide whether this is positive or negative:\r\n" );
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document.write( "Since  is is the 4th quadrant, then \r\n" );
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document.write( "° so multiplying that through by \r\n" );
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document.write( "° \r\n" );
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document.write( "The means  is in quadrant 2.  Since\r\n" );
document.write( "the sine is positive in the 2nd quadrant, the final answer\r\n" );
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document.write( "And of course now that we have the answer we can change\r\n" );
document.write( " back to :\r\n" );
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document.write( "2) What is the solution set of the equation\r\n" );
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document.write( "  =  in the interval ?\r\n" );
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document.write( "Use the identity  to replace  on the\r\n" );
document.write( "left side:\r\n" );
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document.write( "  = \r\n" );
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document.write( "  = \r\n" );
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document.write( " = \r\n" );
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document.write( " = \r\n" );
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document.write( "Now use identity  to\r\n" );
document.write( "replace \r\n" );
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document.write( " = \r\n" );
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document.write( "Factor out \r\n" );
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document.write( "Use the zero-factor principle:\r\n" );
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document.write( "3) Find the solution set of  over the domain °.\r\n" );
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document.write( "Use identity \r\n" );
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document.write( "Multiply through by \r\n" );
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document.write( "Use the zero-factor principle:\r\n" );
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document.write( "Edwin

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