# Find all values of `theta` for which 2sin`theta` = -1 for 0 `<=` `theta` `<=` 2`Pi`

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Given `2sintheta = -1`

`rArr sintheta = -1/2`

Here, the sin of theta is negative. That puts the angle somewhere in the 3rd or 4th quadrant.

Again, `sin 30^o` or `sin(pi/6)=1/2`

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

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

**Therefore, the values of theta are `(7pi)/6` and `(11pi)/6` for** `0` `<=` `theta` `<=` `2pi.`

**Sources:**