Question

use reference angles to find exact value of the expression. sin -2pi/3

Answer 1

Think about the unit circle

Answer 2

What is the angle measure here?

Answer 3

Are you familiar with the ordered pairs on the unit circle ? @dabeezy

Answer 4

-2pi/3 has the same coterminal angle as 4pi/3
So, what is the ordered pair at that angle location?

Answer 5

if in quadrant 1, sin is \(\frac{\sqrt{3}}{2}\) , then you have to ask yourself what the supplementary angle to \(\frac{\pi}{3}\)would give you a negative value of \(\frac{-\sqrt{3}}{2}\)

Answer 6

sorry guys i was on a web site, im here now. i have this worked out. im going to submit my answer. check my work please

Answer 7

Sure, as long as you're posting it here we can :)

Answer 8

i am, just takes a min. have to use phone

Answer 9

@Jhannybean

Answer 10

You have really nice writing, I must say.

Answer 11

thank you

Answer 12

is work correct?

Answer 13

I would have done it like this.

Answer 14

The hand writing is even better than mine! :O

Answer 15

i drew that from this

Answer 16

\[\ 240 \cdot \frac{\pi}{180} = \frac{4\pi}{3}\]\[\sin\left(\frac{4\pi}{3}\right) = -\frac{\sqrt{3}}{2}\]