Question 864490: If cos (2 theta)= 120/169, find cos, sin, and tan
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! If cos (2 theta)= 120/169, find cos, sin, and tan
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cos(2t) = cos^2t-sin^2(t) = cos^2(t)+cos^2(t)-1 = 2cos^2(t)-1
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Equation:
2cos^2(t)-1 = 120/169
2cos^2(t) = (120+169)/169
cos^2(t) = (289)/(338)
cos(t) = sqrt(289)/sqrt(338)
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cos(2t) = 1-2sin^2(t) = 120/169
2sin^2(t) = 49/169
sin^2(t) = 49/338
sin(t) = 7/sqrt(338)
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tan(t) = sin(t)/cos(t) = 7/sqrt(289)
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Cheers,
Stan H.
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