# 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 in several 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:

## 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)