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:
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Derive Half Angle Identities (Algebra)Wumbo (internal)
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Derive Half Angle Identities (Inscribed Angle)Wumbo (internal)
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Derive Half Angle Identities (Complex Plane)Wumbo (internal)