On the Rational Values of Trigonometric Functions of Angles that Are Rational in Degrees.

Fix I n i such that Graph HT <math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mi>n</mi><mi> </mi></mrow></math> ht is an integer multiple of Graph HT <math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><mrow><msup><mrow><mrow><mn>360</mn></mrow></mrow><mo>°</mo></msup></mrow></math> ht . First, we assume that Graph HT <math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mtext>cos</mtext><mo /><mo stretchy="false">(</mo><mi> </mi><mo stretchy="false">)</mo></mrow></math> ht is a rational number different from 0. Suppose that Graph HT <math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mtext>tan</mtext><mo /><mo stretchy="false">(</mo><mi> </mi><mo stretchy="false">)</mo></mrow></math> ht is a rational number. [Extracted from the article]