SOLUTION: Find the exact value of sin 2a, cos 2a, and tan2 a given that: cos a=-2/11 and a is in Quadrant III I need help understanding exactly how to derive the conclusions please.

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Question 467906: Find the exact value of sin 2a, cos 2a, and tan2 a given that:
cos a=-2/11 and a is in Quadrant III
I need help understanding exactly how to derive the conclusions please. I am soo lost.
Answer by stanbon(75887) (Show Source):
You can put this solution on YOUR website!
Find the exact value of sin 2a, cos 2a, and tan2 a given that:
cos a=-2/11 and a is in Quadrant III
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sin(2a) = 2sin(a)cos(a)
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Find sin(a):
Since cos(a) = x/r = -2/11 in QII
x = -2 and r = 11
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Then y = sqrt[11^2-2^2] = sqrt(117]
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So sin(a) = y/r = sqrt(117)/11
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Then sin(2a) = 2(sqrt(117)/11*(-2/11) = -4sqrt(11)/121
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Using sin(a) and cos(a) you can find cos(2a) = cos^2-sin^2
and tan(2a) = sin(2a)/cos(2a)
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Keep in mind that your "a" is in the 2nd Quadrant.
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Cheers,
Stan H.