Square Roots of Integers Expressed with Sines (for sqrt(7) or higher primes)

kinerd518

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Apr 30, 2018
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Hello!

We all learn
sqrt(2) = 2 sin(45°), and
sqrt(3) = 2 sin(60°)

Any integer whose square root is also an integer we can express if we really want to with some multiple of sin(90°).

Once I learned about the golden ratio, and from that that
sqrt(5) = 1 + 4 sin(18°)

My question is, is there any way to express sqrt(7) or higher primes? If so, is there any systematic way to determine them? If not, why not?

Thanks!
 
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