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if csc theta= -5/3 and theta has its terminal side in quadrant III, find the exact value of tan 2 theta.

  • math - ,

    csc(θ)=-5/3
    1/sin(θ)=-5/3
    sin(θ)=1/(-5/3)=-3/5
    cos(θ)=-√(1-(-3/5)²)
    =-4/5
    tan(θ)=sin(θ)/cos(θ)
    =(-3/5)/(-4/5)
    =3/4
    tan(2θ)=2tan(&theta))/(1-tan²(θ))
    =2(3/4)/(1-(3/4)²)
    =3.43
    (note: 2θ is in the first quadrant.

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