How to find a specific function with a set of solutions

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I am trying to find a specific function that takes in 2 numbers(coordinate points on a circle) and outputs some number result. I've attached an image for visual reference. But at the coordinate (1,0) the result has to be -1, at the coordinate (0.7,0.7) the result has to be 0.75, and at the coordinate (0,1) the result has to be 1.

What would be the best way to go about finding the equation for something like this?

visual image of wanted results for each coordinate