csc θ is inverse of sin θ.
sin θ = opposite leg/hypotenuse, so
csc θ= hypotenuse/opposite leg
hypotenuse =√((leg1)² +(leg2)²) =√(6²+8²)=√(36+64)=√100=10
csc θ = 10/8=5/4
cscθ =5/4
sec θ is inverse of cos θ , cos θ =adjacent leg/hypotenuse, so
sec θ =hypotenuse/ adjacent leg =10/6=5/3
sec θ =5/3