Trig Identities Calculator
Explore core trigonometric identities with minimal inputs. Choose an identity, enter angles or a value, then compute results instantly.
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Helping Notes
Only essential fields are shown: an identity choice plus its needed angles or value. Formulas follow standard references. :contentReference[oaicite:1]{index=1}
Results use degrees. Where sign is ambiguous (e.g., Pythagorean partner), the magnitude is shown and ± noted when applicable. :contentReference[oaicite:2]{index=2}
Results
Primary Result
Additional Values
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What Is a Trig Identities Calculator?
A Trig Identities Calculator helps you transform and verify trigonometric expressions by applying standard identities automatically and transparently. Enter an expression (such as or ) and the tool rewrites it step by step into an equivalent, often simpler form. It recognizes angle units, converts between degrees and radians when needed, and can check proposed identities by simplifying the difference between left‑hand side and right‑hand side to zero. This is ideal for homework proofs, exam prep, calculus integrand cleanup, signal processing, and physics problems where compact, exact trigonometric forms save time and reduce algebraic mistakes.
About the Trig Identities Calculator
The calculator knows core Pythagorean, reciprocal, cofunction, even/odd, periodic, sum/difference, double‑angle, half‑angle, and product‑to‑sum identities. It expands or factors expressions intelligently—switching between forms like and , or compressing products using . It also rewrites powers via power‑reduction, rationalizes denominators with trigonometric terms, and handles symbolic parameters alongside numeric evaluation for confidence checks. When verifying an identity, it reports a canonicalized result (e.g., “simplifies to 0 for all permitted x”) and flags domain restrictions such as where or are undefined.
Pythagorean: , ,
Reciprocal: , ,
Cofunction: , ,
Even/Odd & Periodicity: , , ; ,
Sum/Difference: ; ;
Double‑angle: , ,
Half‑angle (power reduction): ,
Product ↔ Sum: ,
Unit conversion:
How to Use This Trig Identities Calculator
- Enter an expression or a pair (LHS and RHS) to verify. Choose degrees or radians for angles.
- Select actions: expand, factor, power‑reduce, convert products to sums, or simplify to a canonical form.
- Compute. The tool applies identities stepwise, shows intermediate lines, and flags domain restrictions for undefined points.
- Copy the simplified result or the proof log for your notes or assignment.
Examples
- Power reduction: Show using ⇒ LHS simplifies to .
- Angle sum: (verify by expansion).
- Evaluate cos 75°: .
- Product to sum: .
Formula Snippets Ready for Rendering
FAQs
What is a trigonometric identity?
An equation true for all permissible variable values, e.g., , unlike an equation that holds only for specific solutions.
How do I verify an identity?
Simplify one side to match the other, or simplify LHS − RHS to 0 while respecting domain restrictions.
Does the calculator support degrees and radians?
Yes—choose your unit. Internally, angles may be converted with .
Why does the tool mention domain restrictions?
Identities exclude points where functions are undefined, e.g., at .
Can it expand or factor expressions automatically?
Yes. It applies sum/difference, product‑to‑sum, and power‑reduction rules to rewrite expressions in the requested form.
Will it show steps?
Yes—each transformation is listed so you can follow the reasoning in a proof or solution.
What’s the difference between simplifying and solving?
Simplifying finds an equivalent form; solving finds variable values that satisfy an equation.
Can it handle symbolic parameters?
Yes, it keeps symbols like and simplifies using identities valid for all real inputs.
How can I avoid common mistakes?
Track angle units, square identities correctly, and watch sign changes in sum/difference formulas.