Question 73914
This problem has an error in it.  It tells you that theta is in the second quadrant,
but it gives you a positive value for the cosine of theta.  You need to recognize that in
the second quadrant the cosine is negative.  Cosine is only positive in quadrants I and IV.
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Here's a way to do the problem quickly using a scientific calculator ($10 type).
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Set you calculator into the degrees mode.  Divide 2 by the square root of 5 and use the
change sign mode to make the answer a negative number.  Your answer should be -0.894427191.
This is the decimal value of the cosine of theta.
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Next use the arccosine function (cos^-1 function which is normally shift+cos keys) and you 
should find that the angle whose cosine is -0.894427191 is 153.4349488 degrees.  Multiply this 
angle by 2 to get two theta. You should have 306.8698976 degrees for 2 theta. (Note that 
this angle is in quadrant IV where the cosine is positive.)  Now that you have found 2 theta, 
just press the cosine key and you should find that the cosine of 2 theta is 0.6 which is the 
same as +3/5.
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Answer d is the correct answer.  
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Hope this helps. Using a calculator makes it go fast.