Expand the Trigonometric Expression sin(x/2)

Problem

sin(x/2)

Solution

1. Identify the half-angle identity for the sine function.

2. Apply the formula for the sine of a half-angle, which relates sin(x/2) to cos(x)

3. Determine the sign based on the quadrant in which the angle x/2 lies. Since the quadrant is not specified, the expression includes a ± symbol.

Final Answer

sin(x/2)=±√(,(1−cos(x))/2)

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