Is square root 1 minus cosine squared theta = −sin θ true? if so, in which quadrants does angle θ terminate?

The trigonometric identity states that the sum of the square of cosine and sin is equal to 1. In this case, the identity is tried to rearrange and tried to verify if the statement above is true. 

Square root 1 minus cosine squared theta = −sin Θ 
This is only true in angles tried such as (360-45) or (270-45). hence  Θ should be in quadrant III and IV only