Confused on what should be negative when finding with half angle

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Is it possible that the value of sin is negative in a half angle

Is it possible that the value of sin is negative in a half angle

Is it possible that the value of sin is negative in a half angle

Why are the x-values [-pi/2, pi/2] here? I thought pi/2 meant 90

Is it possible that the value of sin is negative in a half angle formula? - Quora