Exact value of trig functions Can we find the exact value(not numerical/approximation) of sin 1?
I tried to do so by solving a cubic equation using Cardano formula but I ended up with complex nested radicals): I was told to use other methods but that won't yield exact values
sin(1) is a Transcendental number.
http://en.wikipedia.org/wiki/Transcendental_number
http://en.wikipedia.org/wiki/Lindemann%E2%80%93Weierstrass_theorem

ie ,sin(1) is not a solution  a non-zero polynomial equation with rational coefficients.In other words sin(1) can't be expressed in closed form only using fractions and radicals.
Note: sin(a), where a is algebraic(not transcendental) ,is transcendental.

Does that help you?
Yes, we can. However the radicals will be nested as well as repeating. Using Precise-Rewritten method, exact value of Sin 1 degree is:
 $$√(2 - √(2  + √(2  \overline {+ √(2 + √(2  + √(2 + √(2 - √(2 - √(2 - √(2 + √(2 - √(2  - √(2  + √(2  - √(2}]/2$$

Please care the overline (not fraction) and closing brackets have collapsed by']'.

This method gives exact values of Sine of all integer angles. Please visit https://archive.org/details/ExactTrigonometryTableForAllAnglesFinal for the list.