Pythagorean Theorem problem

Question

Find the exact values of each of the remaining trigonometric functions of theta

sin theta=2 square root of 13 over 13, pi over 2 <theta <pi

Answer 1

Since θ lies in quadrant 2, cosθ < 0.

cosθ = -√(1 - sin²θ) = -(3√13)/13

tanθ = sinθ/cosθ = -2/3

cotθ = 1 / tanθ = -3/2

secθ = 1 / cosθ = -√13/3

cscθ = 1 / sinθ = √13/2