Don't use a calculator and use the rations in the reference triangle.
please explain in detail how you got it!
Do you understand that a "reference triangle" has angles between 0 and $\displaystyle \pi/2$? Also, that sine and cosine are periodic with period [itex]2\pi[/itex]. Once you realize that, it is just elementary arithmetic. What is 23/6 as a mixed fraction?