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Topic: Properties of a right triangle
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Deep Deb

Posts: 420
Registered: 12/6/04
Properties of a right triangle
Posted: Dec 8, 2012 3:09 PM
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Let ABC be a right triangle such that C = pi/2, 0<A<pi/2
Sides a, b are integers and c^2 is an integer but c is not an integer. This implies both Sin A and Cos A are irrational.

Conjecture: Both (sin 5A)^(2/5) and (cos 5A)^(2/5) can not be rational.
Any helpful comment about the conjecture will be appreciated.
If the conjecture is valid can it also be extended for sin 7A and cos 7A?

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