Half Angle Identities

The half angle identities are trigonometric identities that express the sine and cosine of a half-angle in terms of the sine and cosine of a single angle.

The identities can be derived a number of ways.

  • Using the double angle identities and algebra[1]
  • Using the inscribed angle theorem and the unit circle[2]
  • Using the trigonometry of complex numbers[3]

The half angle identities express the cosine and sine of a half-angle in terms of the sine and cosine of the single angle. The identities can be derived using the geometry of the inscribed angle shown below:

Half Angle Identities

References

  1. Derive Half Angle Identities (Algebra)
    Wumbo (internal)
  2. Derive Half Angle Identities (Inscribed Angle)
    Wumbo (internal)
  3. Derive Half Angle Identities (Complex Plane)
    Wumbo (internal)