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Rational Sine and Cosine

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Rational Sine and Cosine

There are infinitely many angles θ between 0º and 90º for which both sin θ and cos θ are rational numbers. Prove this statement.

Hint: Here are some examples:

sin θ
cos θ
3
5
4
5
5
13
12
13
7
25
24
25
9
41
40
41

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Problem by Mr. Twitchell

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