A Convoluted Reciprocal: Upper Secondary Mathematics Competition Question

Using only the trigonometric functions on a calculator, including their inverses (if needed), find a sequence of buttons pressed such that the final result is the reciprocal of the initial input value. Also, for what range of input values does this work?

That is, we are looking for a function f such that f(x) = 1/x and f is a compound function of trigonometric functions and their inverses. We also need to find the domain of f.




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