What is the degree of y in sin y?

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Is it possible to find out the degree of the variable operated in a trigonometric or logarithmic or an exponential function? Asking out of curiosity!

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The degree is defined for non-negative integer powers of the variable (monomials) and for polynomials.

It is not defined for other functions.

Rational fractions (ratio of polynomials) can be considered to have a pair of degrees, and fractional polynomials (with non-integer powers) can be considered to have a non-integer degree, but I am not sure this is standard usage.