I dont even know where to start on this question!!
Evaluate: Sin(2Pi/3) and Cos(2Pi/3)
$\displaystyle \sin \frac {2 \pi}3 = \pm \sin \frac {\pi}3$ and $\displaystyle \cos \frac {2 \pi}3 = \pm \cos \frac {\pi}3$. those values you should know. but how do we figure out the signs? we do that by finding out what quadrant the angle $\displaystyle \frac {2 \pi}3$ is in.
Remember the mnemonic, All Students Take Calculus
if it is in the first quad: sine is positive and cosine is positive
if it is in the second quad: sine is positive and cosine is negative
if it is in the third quad: sine is negative and cosine is negative
if it is in the fourth quad: sine is negative and cosine is positive
so, what's the answer?
what? why is there sine and cosine in your answer? the answers are just numbers.
please type coherently, i'm guessing you mean: $\displaystyle \sin \frac {2 \pi}3 = \frac {\sqrt {3}}2$ and $\displaystyle \cos \frac {2 \pi}3 = - \frac 12$
if so, that's correct
you can keep adding or subtracting $\displaystyle 2 \pi$ if you don't like the size of the angle. you won't change it's value, you just change the number of revolutions to get there. so here, you would realize that $\displaystyle \frac {19 \pi}6 \equiv \frac {7 \pi}6$