The article introduces the reader to some amazing properties of trigonometric functions. It turns out that if the values of the arguments of the functions sin x, cos x, tg x and ctg x, expressed in radians, are algebraic numbers, then the values of these functions are transcendental numbers. Hence, it follows that the values of all angles of the pseudo-Heronian triangle, including the values of all angles of the Pythagoras or Heron triangle, expressed in radians, are transcendental numbers. If the arguments of functions sin x and cos x, expressed in radians, are equal to x = r 2 \pi, where r are rational numbers, then the values of the functions are algebraic numbers. It should be noted that in this case the argument x = r 2\pi is transcendental and, if expressed in degrees, becomes a rational.
This work is licensed under a Creative Commons Attribution 4.0 International License.
Please read the Copyright Notice in Journal Policy.