# Find all (theta) 0<(theta)<2pi, Such that: CSC(theta)= -2

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`cosec(theta) = -2`

we know, `cosec(theta) = 1/sin(theta)` , then,

`1/sin(theta) =-2`

This gives,

`sin(theta) = -1/2`

`theta = sin^(-1)(-1/2)`

`theta = -pi/6`

This is the primary solution, to find the solutions in the given range, we need to know the general solution for sine.

The general solution for sine is,

`theta = npi+(-1)^n(-pi/6)` n is any integer.

n = 0,

`theta = -pi/6`

n =1,

`theta = pi + pi/6 = (7pi)/6`

n = 2,

`theta = 2pi - pi/6 = (11pi)/6`

**Therefore the solutions in the given range, `0lt=theta lt=2pi ` are,**

`(7pi)/6 and (11pi)/6`