For angle in Quadrant III and tan 32 find csc Solutiontan t

For angle in Quadrant III, and tan = (3/2), find csc

tan theta = 3/2

tan theta = perpendicular / base

perpendicular = 3

base = 2

hypotenuse = sqrt ( 3^2 + 2^2) by pythagorean identity

hypotenuse = sqrt 13

csc theta = hypotenuse / perpendicular = sqrt 13 / 3

since its in 3rd quadrant

therefore, csc theta = - sqrt 13 / 3