Question 73914
If (theta) is a second-quadrant with cos(theta)={{{-2/sqrt5}}}, find the exact value of cos2(theta).
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cos(2theta)= cos^2(theta) - sin^2(theta)
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Need to find sin(theta)
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cos(theta) = adj/hyp = 2/sqrt5
adjacent is an x-value; it is negative in the 2nd quadrant;
therefore the cos(theta) is negative; it must be -2/sqrt5
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If adj = -2  and hyp = sqrt5 then opp = sqrt((sqrt5)^2-2^2))= 1
Therefore sin(theta)= opp/hyp = 1/2sqrt5
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Then cos(2theta)= (2/sqrt5)^2 - (1/sqrt5)^2 = 3/5 
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Cheers,
Stan H.