Trig help: What is csc (theta)+2=0

Question

What is cscθ+2=0

Find all solutions of the equation in the interval
0,2π.

 

answer must be in radians in terms of pi (π)

Answer 1

cscθ = 1 / sinθ

 

 

(1 / sinθ) + 2 = 0

 

1 / sinθ = -2

 

sinθ = -1/2

 

 

sine is negative in the 3rd and 4th quadrant.  We know that sin(π/6) is 1/2.

 

θ = π + π/6

   = (6π + π) / 6

   = 7π/6

 

 

 

θ = 2π - π/6

   = (12π - π) / 6

   = 11π/6