We can express values for (e.g. 22,5° or 45° or 54°,90°....) with a combination of square roots and basic calculating operations, however are they all expressible in such a way (=> are all algebraic?) Or are non-obvious trigonometric values (e.g. cos(3°)) transcendental numbers?

With very poor math skills, these are my thoughs on values that are not multiples of 5 or are already known for being algebraic.

All help is appreciated.


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    $\begingroup$ Trig functions of rational multiples of $\pi$ are all algebraic (but not all expressible in radicals), trig functions of rational numbers (in radians) are transcendental (except for trivial, like $0$). $\pi$ radians is equal to $180$ degrees, just in case $\endgroup$ – Yuriy S Nov 4 '16 at 19:23
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    $\begingroup$ You may find this link relevant $\endgroup$ – MPW Nov 4 '16 at 19:26
  • $\begingroup$ Thank you both so much! I found the link very releant indeed! $\endgroup$ – Harley Potter Nov 5 '16 at 13:55

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