Find the exact value of sine, start fraction, 4, pi, divided by, 3, end fractionsin 34π​ in simplest form with a rational denominator.

The given angle is 4π/3.

Step 1: Convert the angle to a value between 0 and 2π.

4π/3 is already between 0 and 2π, so no conversion is necessary.

Step 2: Determine the quadrant of the angle.

4π/3 is in the third quadrant, where sine is negative.

Step 3: Find the reference angle.

The reference angle is π/3.

Step 4: Find the exact value of sine for the reference angle.

sin(π/3) = √3/2

Step 5: Apply the sign based on the quadrant.

Since 4π/3 is in the third quadrant where sine is negative, the exact value of sin(4π/3) is -√3/2.