Question 921495: Given that cosx= -12/37 and x is in Quadrant 3, determine sin2x, cos2x, and tan2x. Which quadrant is 2x in?
Answer by lwsshak3(11628)   (Show Source):
You can put this solution on YOUR website! Given that cosx= -12/37 and x is in Quadrant 3, determine sin2x, cos2x, and tan2x. Which quadrant is 2x in?
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cosx=-12/37
x≈251.08˚
2x≈142.15˚
sinx=-√(1-cos^2x)=-√(1-144/1369)=-√(1225/1369)=-35/37
..
sin2x=2sinxcosx=2*-35/37*-12/37=840/1369
cos2x=cos^2x-sin^2x=(-12/37)^2-(-35/37)^2=144/1369-1225/1369=-1081/1369
tan2x=sin/cos=840/-1081=-840/1081
..
calculator check:
sin2x=sin(142.15)≈0.6136
exact value=840/1369≈0.6136
..
cos2x=cos(142.15)≈-0.7896
exact value=-1081/1369≈-0.7896
..
tan2x=tan(142.15)≈-0.7770
exact value=-840/1081≈-0.7770
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