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Half angle

This original textbook reading covers part of the AP topic. Follow the AP course outline for complete topic instruction and practice.

Half angle

$\sin (\frac{a}{2}) = \sqrt{\frac{1 - \cos x}{2}}$

$\cos (\frac{a}{2}) = \sqrt{\frac{1 + \cos x}{2}}$

$\tan (\frac{a}{2}) = \frac{\sin x}{1 + \cos x} = \frac{1 - \cos x}{\sin x}$

Related Glossary Terms

Angle addition, Double Angle, Hopscotch discontinuity, Trigonometric identities, Trigonometric substitution

Index

Chapter 1 - An Overview of Trigonometry

Glossary and deeper reading · 1 refreshers

These editorial refreshers supplement the reading. Definitions and examples are added guidance; original source wording and recorded answers remain in their original context.

Half angle identity
A half angle identity expresses a trigonometric function of half an angle using the original angle. For example, sin²(θ/2)=(1−cos θ)/2. Taking a square root gives a magnitude, and the sign of sin(θ/2) depends on the angle’s quadrant. For θ=π, the formula yields sin(π/2)=1 using the positive sign.

Half angle identity

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