LaTeX
\sin^2\theta+\cos^2\theta=1Variables
- θ: angle
How to use this formula
Relates sine and cosine for the same angle.
Important notes
- The identity comes from the unit circle.
- Rearrange it to replace sin²θ or cos²θ.
Quick example
If sinθ=3/5 in the first quadrant, cosθ=4/5.
Applicability, worked calculation, and verification
Assumptions and domain checks
- The identity comes from the unit circle.
- 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
If sinθ=3/5 in the first quadrant, cosθ=4/5.
Common mistakes
- Do not mix degrees and radians in Pythagorean Trigonometric Identity; use one angle convention throughout the calculation.
- Verify the result of Pythagorean Trigonometric Identity with a known case, inverse operation, dimensional check, or independent calculation before publishing it.
Continue the workflow
Use Pythagorean Trigonometric 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+\cos^2\theta=1. - 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 Pythagorean Trigonometric Identity used for?
Relates sine and cosine for the same angle.
Can I copy this formula as LaTeX?
Yes. Copy \sin^2\theta+\cos^2\theta=1 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.