Rational values for sine, cosine, and tangent
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What are the possible combinations of sine, cosine, and tangent values such that all three are simultaneously rational? I am aware of the below two cases. $sin(x) = 0, cos(x) = 1, tan(x) = 0$ is a trivial case for angle measure zero $sin(x) = 0.6, cos(x) = 0.8, tan(x) = 0.75$ is another case, for an angle of $37$ degrees (approximately) Are there any other combinations that satisfy the condition? If not, is it possible to prove that these are the only possible combinations?
algebra-precalculus trigonometry rational-numbers rationality-testing
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edited 43 mins ago
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