SOLUTION: Find the exact values of sin(2u), cos(2u), and tan(2u) using the double-angle formulas.
cos(u) = −1/7,pi/2<u<pi
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-> SOLUTION: Find the exact values of sin(2u), cos(2u), and tan(2u) using the double-angle formulas.
cos(u) = −1/7,pi/2<u<pi
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Question 867571: Find the exact values of sin(2u), cos(2u), and tan(2u) using the double-angle formulas.
cos(u) = −1/7,pi/2 Answer by lwsshak3(11628) (Show Source):
You can put this solution on YOUR website! Find the exact values of sin(2u), cos(2u), and tan(2u) using the double-angle formulas.
cos(u) = −1/7,pi/2
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Interval: [0,3π/2]
cos(u)=-1/7 (In quadrant II)
tan(u)=sin(u)/cos(u)=√48/-1=-√48
...
sin(2u)=2sin(u)cos(u)=2√48/7*(-1/7)=-(2√48)/49
cos(2u)=cos^2(u)-sin^2(u)=1/49-48/49=-47/49
tan(2u)=2tan(u)/1-tan^2(u)=-2√48/(1-48)=2√48/47
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Calculator check:
cos(u)=-1/7
u≈98.21˚
2u≈196.42˚
...
sin(2u)≈sin(196.42)≈-0.2827…
Exact value=-(2√48)/49≈-0.2827…
..
cos(2u)≈cos(196.42)≈-0.9591…
Exact value=-47/49≈-0.9591…
..
tan(2u)≈tan(196.42)≈-0.2948…
Exact value=-(2√48)/47≈-0.2948…
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