SOLUTION: find sin2x, cos2x, and tan2x if sinx= {{{-2/sqrt(5)}}} and x terminates in quadrant III

Algebra ->  Trigonometry-basics -> SOLUTION: find sin2x, cos2x, and tan2x if sinx= {{{-2/sqrt(5)}}} and x terminates in quadrant III      Log On


   

Question 856628: find sin2x, cos2x, and tan2x if sinx= -2%2Fsqrt%285%29 and x terminates in quadrant III
Answer by lwsshak3(11628) About Me  (Show Source):
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find sin2x, cos2x, and tan2x if sinx= -2%2Fsqrt%285%29 and x terminates in quadrant III
cos(x)=-√(1-sin^2(x))=-√(1-4/5)=-√(1/5)=-1/√5
tan(x)=sin(x)/cos(x)=-1/-2=1/2
..
sin(2x)=2sin(x)cos(x)=2*-2/√5*-1/√5=4/5
cos(2x)=cos^2x-sin^2(x)=(1/5)-4/5=-3/5
tan(2x)=2tan(x)/(1-tan^2(x))=2*(1/2)/(1-(1/2)^2)=1/(3/4)=4/3
..
Calculator check:
sinx=-2/√5
x≈243.43˚
2x≈486.87
sin(2x)≈sin(486.87)≈0.7999…
Exact value=4/5=0.8000
..
cos(2x)=cos(486.87)≈-0.6000…
Exact value=-3/5=-0.6000
..
tan(2x)=tan(486.87)≈-1.3333…
Exact value=4/3≈1.3333…