The terminal ray of angle ∅ drawn in standard position passes through (2,-3). What is the value of csc ∅?

Answer 1

The triangle formed has a hypotenuse we can calculate using the Pythagorean Theorem. h = √(2² +(-3)²) = √13

csc(∅) = hypotenuse/opposite so, in this case csc = √13/-3

Answer 2

Draw and label a diagram.

sin θ = -3 / √13

csc θ = -√13 / 3