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Double Angle Formulas Calculator

Online double-angle calculator: enter α to find sin2α and cos2α; the special case of the addition formula with β=α, also used for power reduction.

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sin2α=2sinαcosα; cos2α=2cos²α−1
In degrees

📖 Tutorial | Double Angle

1. Definition
Setting β=α in the addition formula: sin2α=2sinαcosα, cos2α=cos²α−sin²α=2cos²α−1=1−2sin²α.
2. Formula & Notation
αOriginal angle
2αDouble angle
3. Properties & Laws
  • sin2α=2sinαcosα;
  • cos2α has three equivalent forms;
  • tan2α=2tanα/(1−tan²α);
  • Power reduction: sin²α=(1−cos2α)/2.
4. Steps
  1. Enter α (degrees);
  2. Click "Calculate";
  3. Or click "Load Example".
5. Worked Examples
Example: α=30° gives sin60≈0.8660, cos60=0.5.
6. Common Pitfalls
sin2α≠2sinα in general;
Choose among the three cosine forms;
Keep power-reduction coefficients right.

❓ FAQ | Double Angle

Sine?
2sinαcosα.
Cosine forms?
cos²−sin², 2cos²−1, 1−2sin².
Tangent?
2tanα/(1−tan²α).
Equal 2sinα?
No.
Power reduction?
sin²α=(1−cos2α)/2.
Origin?
Addition formula with β=α.
Uses?
Simplify, reduce powers.