What are the sine, cosine, and tangent values of 2π/3 radians?

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Trigonometric Values of 2π/3 Radians

The angle 2π/3 radians is in the second quadrant of the unit circle. To find the sine, cosine, and tangent values of this angle, we can refer to the corresponding values from the reference angle.

Reference Angle

The reference angle for 2π/3 is given by:

  • Reference angle = π – 2π/3 = π/3

Trigonometric Values

Sine

The sine of an angle in the second quadrant is positive. Therefore, we have:

  • sin(2π/3) = sin(π/3) = √3/2

Cosine

The cosine of an angle in the second quadrant is negative. Thus, we find:

  • cos(2π/3) = -cos(π/3) = -1/2

Tangent

The tangent function is the ratio of sine to cosine. Therefore:

  • tan(2π/3) = sin(2π/3) / cos(2π/3) = (√3/2) / (-1/2) = -√3

Summary of Trigonometric Values

  • sin(2π/3) = √3/2
  • cos(2π/3) = -1/2
  • tan(2π/3) = -√3

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