• Oct 2nd 2007, 05:45 PM
redpanda11
I dont even know where to start on this question!!

Evaluate: Sin(2Pi/3) and Cos(2Pi/3)
• Oct 2nd 2007, 05:49 PM
Jhevon
Quote:

Originally Posted by redpanda11
I dont even know where to start on this question!!

Evaluate: Sin(2Pi/3) and Cos(2Pi/3)

$\sin \frac {2 \pi}3 = \pm \sin \frac {\pi}3$ and $\cos \frac {2 \pi}3 = \pm \cos \frac {\pi}3$. those values you should know. but how do we figure out the signs? we do that by finding out what quadrant the angle $\frac {2 \pi}3$ 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

• Oct 2nd 2007, 06:12 PM
redpanda11
sin root 3/2,
cos -1/2?
• Oct 2nd 2007, 06:23 PM
redpanda11
sin + pi/3, cos -pi/3
• Oct 2nd 2007, 06:26 PM
Jhevon
Quote:

Originally Posted by redpanda11
sin root 3/2,
cos -1/2?

please type coherently, i'm guessing you mean: $\sin \frac {2 \pi}3 = \frac {\sqrt {3}}2$ and $\cos \frac {2 \pi}3 = - \frac 12$

if so, that's correct

Quote:

Originally Posted by redpanda11
sin + pi/3, cos -pi/3

:confused:
• Oct 2nd 2007, 06:30 PM
redpanda11
sorry i meant root3/2
and -1/2
• Oct 2nd 2007, 06:32 PM
redpanda11
sorry!! i understand it to a certain extent but what if it's like tan 19pi/6 how do you know what quadrant it is in??
• Oct 2nd 2007, 06:36 PM
Jhevon
Quote:

Originally Posted by redpanda11
sorry!! i understand it to a certain extent but what if it's like tan 19pi/6 how do you know what quadrant it is in??

you can keep adding or subtracting $2 \pi$ 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 $\frac {19 \pi}6 \equiv \frac {7 \pi}6$