Question

See attached? No clue how to do this!

Answer 1

given tan x= - 3/4 (using x instead of theta)
(tanx)^2 = 9/16

Answer 2

(secx)^2= 1+(tanx)^2 1+9/16 =25/16

secx = +5/4 or - 5/4 but as theta is in 4th quadrant hence secx = +5/4
hence cosx =+4/5

Answer 3

now (tanx)^2 = 9/16
or (cotx)^2 = 16/9
(cosecx)^2 = 1 +(cotx)^2
(cosecx)^2 = 1+16/9
(cosecx)^2 = 25/9
hence cosecx = +5/3 or -5/3
but as theta is in 4th quadrant hence cossecx = - 5/3