Dot product with a difference maximum angle

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In a program I'm making I use the dot product to get a value between 1 and 0 dependent on the angle between two vectors. The value is 0 if the vectors are parallel and 1 if they are perpendicular. What I am looking for now, is a way to have an extra variable which defines the angle at which this value should be maximal(1), instead of always using 90 degrees.

Thanks in advance.