Let (theta) be an angle in quadrant II such that csc(theta)=8/5 Find the exact value of tan(theta) and cos(theta).

Answer 1

if csc Ø = 8/5
then
sin Ø = 5/8
I see a right-angled triangle with hypotenuse 8 and vertical side (the y) of 5
By Pythagoras, the other side is √39

in II both cosine and tangent are negative, so
tanØ = -5/√39
cosØ = -√39/8