To find the sine, cosine, and tangent of 2π/3 radians, we can start by identifying the angle in terms of the unit circle.
The angle 2π/3 radians is equivalent to 120 degrees. This angle is located in the second quadrant of the unit circle.
In the second quadrant:
- The sine value is positive.
- The cosine value is negative.
- The tangent value is negative.
To calculate the values:
- The reference angle for 2π/3 is π/3 radians (or 60 degrees).
- Using known values:
- sin(π/3) = √3/2
- cos(π/3) = 1/2
Applying these values to our angle:
- sin(2π/3) = sin(π – π/3) = sin(π/3) = √3/2
- cos(2π/3) = cos(π – π/3) = -cos(π/3) = -1/2
- tan(2π/3) = tan(π – π/3) = -tan(π/3) = -√3
Thus, the final results are:
- sin(2π/3) = √3/2
- cos(2π/3) = -1/2
- tan(2π/3) = -√3