Half sine

Calculus Level 4

Notably, the area under the curve y=sin(x)y=\sin(x) over a semiperiod is exactly 2 since 0πsin(x)dx=cos(x)0π=2.\int_0^\pi\sin(x)\,dx=-\cos(x)\Big|_0^\pi=2. Naturaly then, there is a point (0,A)(0,A) on the yy-axis such that a horizontal line through it divides the above area into two regions of area 1, as shown.

What is A?A?

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