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

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))/(1tan²(θ))
=2(3/4)/(1(3/4)²)
=3.43
(note: 2θ is in the first quadrant.