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In page Algebraic number:

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  • Polynomial roots that cannot be expressed in terms of the basic arithmetic operations and extraction of nth roots (such as the roots of x5 − x + 1). That happens with many but not all polynomials of degree 5 or higher.
  • Values of trigonometric functions of rational multiples of π (except when undefined): for example, cos π/7, cos 3π/7, and cos 5π/7 satisfy 8x3 − 4x2 − 4x + 1 = 0. This polynomial is irreducible over the rationals and so the three cosines are conjugate algebraic numbers. Likewise, tan 3π/16, tan 7π/16, tan 11π/16, and tan 15π/16 satisfy the irreducible polynomial x4 − 4x3 − 6x2 + 4x + 1 = 0, and so are conjugate algebraic integers. This is the equivalent of angles which, when measured in degrees, have rational numbers.[citation needed]