Calculate sine, cosine, and tangent of half an angle using trigonometric identities.
Input Angle
Trigonometric Values
0.5000
sin(θ/2)
Exact and decimal results for θ/2.
cos(θ/2)0.8660
tan(θ/2)0.5774
About this calculator
What are Half-Angle Formulas?
The half-angle formulas allow you to find the trigonometric values for half of a given angle. These are derived from the double-angle formulas and power-reduction identities.
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Pro Tips
The sign (±) depends on the quadrant in which the angle θ/2 lies.
tan(θ/2) can also be expressed as sinθ / (1 + cosθ) or (1 - cosθ) / sinθ.
These formulas are essential in calculus for integration involving trigonometric power reduction.
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Fun Facts
"Trigonometry was developed by astronomers to calculate the distances to stars and the size of the Earth."
"The word 'sine' comes from the Latin 'sinus', meaning 'bay' or 'curve'."
"Half-angle formulas were historically used to create high-precision trigonometry tables by hand."
