Find the solution of the equation in the interval [0,2π).

Question

Find the solution of the equation in the interval [0,2π).

csc0+2=0

write answer in radians in terms of π.

Answer 1

cscθ = -2, so sinθ = -1/2.

sinθ is negative in quadrants 3 and 4.

sin(π/6) = 1/2

Solution in quadrant 3: θ = π + π/6 = 7π/6

Solution in quadrant 4: θ = 2π π/6 = 11π/6

Solution set {7π/6, 11π/6}