Double Angle & Half Angle Calculator
Apply the double-angle and half-angle identities to any input angle.
Enter Angle
Returns sin/cos/tan of 2θ and θ/2
Results
Enter an angle and click calculate.
Identities used
• sin 2θ = 2 sin θ cos θ
• cos 2θ = cos²θ − sin²θ
• tan 2θ = 2 tan θ / (1 − tan²θ)
• sin(θ/2) = ±√((1 − cos θ)/2)
• cos(θ/2) = ±√((1 + cos θ)/2)
Frequently Asked Questions
What are the double angle formulas?▾
sin 2θ = 2 sin θ cos θ; cos 2θ = cos²θ − sin²θ (also = 2cos²θ − 1 = 1 − 2sin²θ); tan 2θ = 2 tan θ / (1 − tan²θ).
What are the half angle formulas?▾
sin(θ/2) = ±√((1 − cos θ)/2); cos(θ/2) = ±√((1 + cos θ)/2); tan(θ/2) = sin θ/(1 + cos θ).
How do you choose the sign?▾
The sign of the half-angle result depends on the quadrant where θ/2 lies. The calculator picks the sign matching the direct numerical value.
When are these used?▾
They're central to integration in calculus, simplifying trig expressions, and solving equations where the unknown appears as a doubled or halved angle.