document.write( "Question 237416: Find the reference angles \"theta\" or ϴ for the angles given below. Find the quadrants in which the angles lie. In addition, show all the steps for deriving the answer. \r
\n" ); document.write( "\n" ); document.write( "1. ϴ = 50° \r
\n" ); document.write( "\n" ); document.write( "2. ϴ = 120°\r
\n" ); document.write( "\n" ); document.write( "3. ϴ = \"7pi%2F6\"\r
\n" ); document.write( "\n" ); document.write( "4. ϴ = 3.3\r
\n" ); document.write( "\n" ); document.write( "5. ϴ = 300°\r
\n" ); document.write( "\n" ); document.write( "6. ϴ = –145° \n" ); document.write( "
Algebra.Com's Answer #174613 by Edwin McCravy(20062)\"\" \"About 
You can put this solution on YOUR website!
Find the reference angles \"theta\" or ϴ for the angles given below. Find the quadrants in which the angles lie. In addition, show all the steps for deriving the answer.
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document.write( "The upper right hand quarter of the graph is QI (the first\r\n" );
document.write( "quadrant)\r\n" );
document.write( "The upper left hand quarter of the graph is QII (the second\r\n" );
document.write( "quadrant)\r\n" );
document.write( "The lower left hand quarter of the graph is QIII (the third\r\n" );
document.write( "quadrant)\r\n" );
document.write( "The lower right hand quarter of the graph is QIV (the fourth\r\n" );
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document.write( "The actual angle ϴ is the angle of rotation beginning\r\n" );
document.write( "at the right hand side of the x-axis (the initial side)\r\n" );
document.write( "and swinging counter-clockwise around to the terminal side\r\n" );
document.write( "when the measure of the actual angle ϴ is positive, and \r\n" );
document.write( "swinging clockwise around to the terminal side when the\r\n" );
document.write( "measure of the actual angle ϴ is negative. \r\n" );
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document.write( "The reference angle of ϴ is the nearest angle taken \r\n" );
document.write( "positive, to the x-axis.\r\n" );
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document.write( "In each case below the blue arc represents the actual \r\n" );
document.write( "angle ϴ, and the green arc represents the reference angle.\r\n" );
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\n" ); document.write( "1. ϴ = 50°
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document.write( "Here ϴ is in QI and its reference angle is also 50°.\r\n" );
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\n" ); document.write( "2. ϴ = 120°
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document.write( "Here ϴ is in QII and its reference angle is 60°, gotten\r\n" );
document.write( "by subtracting 120° from 180°.\r\n" );
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\n" ); document.write( "3. ϴ = \"7pi%2F6\"
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document.write( "This is in radians and is a special angle.  We change to \r\n" );
document.write( "degrees by multiplying by \"%22180%B0%22%2Fpi\".\r\n" );
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document.write( "\"7pi%2F6\"\"%22%D7%22\"\"%22180%B0%22%2Fpi=%22210%B0%22\"\r\n" );
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document.write( "Here ϴ is in QIII and its reference angle in radians\r\n" );
document.write( "is \"pi%2F6\", gotten by subtracting \"pi\" from \"7pi%2F6\" \r\n" );
document.write( "like this:\r\n" );
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document.write( "\"7pi%2F6+-+pi+=+7pi%2F6+-+6pi%2F6+=+pi%2F6\"\r\n" );
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\n" ); document.write( "4. ϴ = 3.3
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document.write( "This is also in radians, but it is not a special\r\n" );
document.write( "angle.  It is a little more than \"pi=3.1416\"\r\n" );
document.write( "radians, which is a little more than 180°.  So\r\n" );
document.write( "we draw the angle a little into QIII:\r\n" );
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document.write( "Here ϴ is in QIII and the reference angle is \"0.1584\"\r\n" );
document.write( "gotten by subtracting \"pi\" from \"3.3\" like this:\r\n" );
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document.write( "\"3.3-pi=3.3-3.1416=.1584\"\r\n" );
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\n" ); document.write( "5. ϴ = 300°
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document.write( "Here ϴ is in QIV and its reference angle is 60°, gotten\r\n" );
document.write( "by subtracting 300° from 360°.\r\n" );
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\n" ); document.write( "6. ϴ = –145°
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document.write( "This is a negative angle so it swings clockwise from\r\n" );
document.write( "the right side of the x-axis like this:\r\n" );
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document.write( "Here ϴ is in QIII and its reference angle is 35°, gotten\r\n" );
document.write( "by subtracting 145° from 180°.\r\n" );
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document.write( "Edwin
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