If cos theta4sqrt41 and theta lies in quadrant 4 find csc th

If cos theta=4/sqrt(41) and theta lies in quadrant 4 find csc theta

Solution

cos theta=4/(41)

adjacent side =4 , hypotenuse =41

opposite side²+adjacent side²=hypotenuse²

opposite side²+4²=(41)²

opposite side²=41-16

opposite side²=25

opposite side=5

csc(theta) = hypotenuse /opposite side, csc(theta) is negative in quadrant 4

csc(theta) = -(41)/5