how do i find sin of 2pi/3?

Question

no calculator
just that table of special vaules and ASTC

Answer 1

Well, you know that 2pi/3 is in the second quadrant, therefore sine will be positive. It's reference angle will be pi - 2pi/3 which is equal to pi/3.

Sin(pi/3) = sqrt(3)/2

Answer 2

I don't konw what that table or ASTC is, but here's how I'd do it:
First, PI is 180 degrees., so 2/3 PI is 120 degrees.

We also know that sin(any angle) is the vertical component, so that 120 degrees has the same sine as 60 degrees (both are 30 degrees from vertical, or 60 degrees from horizontal). I think this is what the "ASTC" part is for - to help you equate angles anywhere with angles between 0 and 90 degrees.

So, does your table have values for the sine of angles like 30, 45, 60, etc.? If so, it will tell you that the sine of 60 degrees is .866.

Answer 3

Look in your table of special values under sin (2pi/3). It should show sqrt(3)/2.

Answer 4

Sin(2pi/3)= Sin((pi/2)+(pi/6))= ...

But Sin(A+B)=SinACosB+ SinBCosA
and Sin(pi/2)=1; Cos(pi/2)=0

Thus
... = Sin(pi/2)Cos(pi/6) + Sin(pi/6)Cos(pi/2) =
= Cos(pi/6)

Now Cos(pi/6)=(3)^(1/2)/2

Then

Sin(2pi/3) = sqrt(3)/2, (sqrt(3)=(3)^(1/2))

Answer 5

Do you know the unit circle? Just use that...

sin 2pi/3 = (sqrt3)/2