# How do you find the 6 trigonometric functions for 5pi/3?

$5 \frac{\pi}{3}$ = 300 = 360 - 60 = 2$\pi$ - $\frac{\pi}{3}$
sin ( 2$\pi$ - $\frac{\pi}{3}$ ) = - sin $\frac{\pi}{3}$ = sqrt3 / 2
Similarly Cos ( 2$\pi$ - $\frac{\pi}{3}$ ) = cos$\frac{\pi}{3}$ = 1/2.
tan ( 2$\pi$ - $\frac{\pi}{3}$ ) = - tan$\frac{\pi}{3}$ = - $\sqrt{3}$
Taking reciprocals we can compute Cosec $5 \frac{\pi}{3}$ = - 2 / sqrt 3'
sec $5 \frac{\pi}{3}$ = 2, cot $5 \frac{\pi}{3}$ = - 1 / sqrt 3.