LaTeX
\sin(2\theta)=2\sin\theta\cos\thetaVariables
- θ: angle measured consistently
How to use this formula
Rewrites the sine of a doubled angle as a product.
Important notes
- The identity holds for degrees or radians when the same unit is used throughout.
- It follows from the sine addition formula.
Quick example
For θ=30°, sin60°=2 sin30° cos30°=√3/2.
Applicability, worked calculation, and verification
Assumptions and domain checks
- The identity holds for degrees or radians when the same unit is used throughout.
- The angle unit and the domain or branch of any inverse trigonometric function must be explicit.
- Use a consistent angle unit and verify the quadrant, periodicity, and domain restrictions of inverse functions.
Worked example
For θ=30°, sin60°=2 sin30° cos30°=√3/2.
Common mistakes
- Do not mix degrees and radians in Sine Double-Angle Identity; use one angle convention throughout the calculation.
- Verify the result of Sine Double-Angle Identity with a known case, inverse operation, dimensional check, or independent calculation before publishing it.
Continue the workflow
Use Sine Double-Angle Identity in your own work
- Check the domainMatch the variables and assumptions to the problem before substituting values.
- Copy the exact notationPreserve grouping, signs, and exponents in
\sin(2\theta)=2\sin\theta\cos\theta. - Edit or convertOpen the expression in the LaTeX editor, then export it for your document or web page.
Review and verification
Last reviewed: 2026-07-23
Automated quality check: Kept noindex until the missing evidence is supplied.
Formula references
- Algebra and Trigonometry 2eOpenStax, Rice University — Reviewed algebra, functions, sequences, trigonometry, and analytic geometry definitions and examples.
Frequently asked questions
What is the Sine Double-Angle Identity used for?
Rewrites the sine of a doubled angle as a product.
Can I copy this formula as LaTeX?
Yes. Copy \sin(2\theta)=2\sin\theta\cos\theta or open it in the LaTeX editor.
What should I check before using it?
Confirm that each variable, unit, domain restriction, and assumption matches the problem.