# Trigonometric functions of rational numbers are algebraic numbers!

Geometry Level 5

What is the degree $$n$$ of the minimal polynomial for $$\tan(1^\circ)$$?

Definition: The minimal polynomial for an algebraic number $$x$$ is the monic polynomial $$f$$ of degree $$n$$ such that $$f(x) = 0$$, $$f$$ has rational coefficients, and for any $$f_1$$ such that $$f_1(x) = 0$$ and $$f_1$$ has rational coefficients, $$\deg(f_1) \geq \deg(f)$$.

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