if u know cos(T), how do u find cos(T/3)? (without using series)?

Question

I know u have to solve the equation 4cos^3(T/3)-3cos(T/3)-cos(T)=0 (solving for cos(T/3)), but what is the real solution?

Answer 1

If you replace cos(T/3) by x and cosT (which you already know) by k you have the equation
4x^3 - 3x - k = 0.
Now the solution of cubic equations is very difficult except in special cases. You may need numerical techniques.

Try putting "solving cubic equations" into google.

Answer 2

The classic way to solve cubic equations is "Cardano's Formula".

There's a newer and easier way, but googling on that phrase and "cubic" or something should get you very close to the best answer.