If cot theta= -24/7 and cos theta < 0, name the quadrant in which theta lies, then find the exact value of csc theta

Answer 1

quadrant II

cot(theta) =-24/7 = adjacent side over opposite side, hypotenuse = 25 (sqr(24^2+7^2)) 25^2 = 625 = 24^2 + 7^2 = 576+49

csc(theta) = 1/sin(theta) = 1/opposite side over hypotenuse = 1/7/25

csc(theta) = hypotenuse over opposite side= 25/7