Trig Helppppp Please!!!

**redpanda11** · October 2nd 2007, 04:45 PM

I dont even know where to start on this question!!

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

**Jhevon** · October 2nd 2007, 04:49 PM

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

so, what's the answer?

**redpanda11** · October 2nd 2007, 05:12 PM

sin root 3/2,
cos -1/2?

**redpanda11** · October 2nd 2007, 05:23 PM

sin + pi/3, cos -pi/3

**Jhevon** · October 2nd 2007, 05:26 PM

Originally Posted by redpanda11

sin root 3/2,
cos -1/2?

what? why is there sine and cosine in your answer? the answers are just numbers.

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

Originally Posted by redpanda11

sin + pi/3, cos -pi/3

**redpanda11** · October 2nd 2007, 05:30 PM

sorry i meant root3/2
and -1/2

**redpanda11** · October 2nd 2007, 05:32 PM

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??

**Jhevon** · October 2nd 2007, 05:36 PM

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 $\frac {19 \pi}6 \equiv \frac {7 \pi}6$

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