If csc (theta) = -4/3, then csc (-theta) = ?

Answer 1

csc θ = 1 / sin θ

csc -θ = 1 / sin -θ

sin -θ = - sin θ

csc -θ = -1 / sin θ

csc -θ = -csc θ

Answer 2

cosecant, like its reciprocal sine, is an odd function meaning that f(-x) = -f(x).

So since csc(θ) = -4/3, then -csc(θ) = - -4/3 = 4/3 so csc(-θ) = 4/3