Question 919538: Find sin2x,cos2x,tan2x if sinx=3/sqrt10 and x terminates in quadrant I
Answer by lwsshak3(11628)   (Show Source):
You can put this solution on YOUR website! Find sin2x,cos2x,tan2x if sinx=3/sqrt10 and x terminates in quadrant I
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cosx=√(1-sin^2x)=√(1-9/10)=√(1/10)=1√10
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sin2x=2sinxcosx=2*3/√10*1/√10=6/10=3/5
cos2x=cos^2x-sin^2x=1/10-9/10=-8/10=-4/5
tan2x=sin2x/cos2x=3/-4=-3/4
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Check:
sinx=3/√10
x=71.565
2x=143.13
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sin2x=sin(143.13)=0.6000
exact value as computed=3/5=0.6000
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cos2x=cos(143.13)≈.0.7999
exact value as computed=4/5=0.8000
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tan2x=tan(143.13)≈-0.7500
exact value as computed=-3/4=-0.7500
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