Find the closet solution and interval solutions of the following

Question

tan(θ)=5

csc(x)+8=5

Answer 1

tan x = 5

x = the angle whose tangent is 5 which is 78.69 degrees or 258.69 degrees or 78.69 + 180n where n equals any integer. x is in the 1st or 3rd quadrants.

cscx = -3 = 1/sinx = -3

sinx = -1/3 placing x in the 3rd or 4th quadrants

x = -19.47 degrees, or 160.53 degrees or -19.47 + 360n degrees where n is any integer or 160.53 degrees + 360n where n equals any integer.