Prove Trig Identity Calculator

Compare both sides through guided trigonometric checks. Spot likely identities and risky domains before sharing. Download clean reports for class, tutoring, or revision tasks.

Calculator Inputs

Use sin(x), cos(x), tan(x), sec(x), csc(x), cot(x), sqrt(x), abs(x), pi, e, and ^ for powers.

Example Data Table

Left Side Right Side Main Formula Expected Result
sin(x)^2 + cos(x)^2 1 Pythagorean identity Likely identity
tan(x) sin(x) / cos(x) Quotient identity Likely identity
sec(x) 1 / cos(x) Reciprocal identity Likely identity
1 + tan(x)^2 sec(x)^2 Pythagorean identity Likely identity

Formula Used

The calculator tests whether both sides give the same value across many sample points.

Difference = absolute value of left side minus right side

Identity likely true when maximum difference is less than or equal to tolerance

Common Trigonometric Rules

How To Use This Calculator

  1. Enter the left side of the identity.
  2. Enter the right side of the identity.
  3. Choose radians or degrees.
  4. Set tolerance and sample count.
  5. Press the prove button.
  6. Review valid tests, skipped points, and rewrite hints.
  7. Download the result as CSV or PDF when needed.

About The Prove Trig Identity Calculator

A trigonometric identity looks simple when both sides match. The work becomes harder when the expression is long. This calculator helps you compare two sides with a careful numerical proof check. It does not replace a written proof. It gives strong evidence, rewrite hints, and domain warnings.

The tool tests both expressions at many safe sample values. It converts supported functions into a controlled expression. Then it compares the left side and right side. A very small difference means the identity is likely true on the tested domain. A large difference suggests the statement is not an identity.

Use standard identities before you trust any result. Reciprocal rules change secant, cosecant, and cotangent. Quotient rules change tangent and cotangent. Pythagorean identities are also common. The calculator lists these formulas below, so you can connect the result with a written solution.

Domain is important. Some values make tangent, secant, cosecant, or cotangent undefined. Division by zero can also happen. The checker skips unsafe points and reports how many valid tests were used. If too many points fail, inspect the original expressions.

For best results, enter one variable only. Use x as the default variable. Put powers with the caret sign. Write sin(x)^2 instead of sin2x. Use clear parentheses around fractions and products. This keeps the parser simple and safer.

The tolerance setting controls strictness. A smaller tolerance is harder to pass. A larger tolerance is more forgiving when decimals are involved. The default value works well for most classroom identities.

The CSV export is useful for spreadsheets. The PDF export is useful for reports. Both exports include the compared sides, test status, maximum difference, and notes. Teachers can save examples for lessons. Students can keep practice records.

Always finish with algebra. Use the calculator to find confidence. Then write transformations step by step. Start from one side. Apply a valid formula. Simplify until it equals the other side.

Advanced options help with mixed lessons. You can choose radians or degrees, change sample density, and set a custom variable name. These controls make the checker useful for basic examples and tougher identities. Keep notes, compare trials, and review mistakes after each test. This habit builds cleaner proofs over time slowly.

FAQs

1. Can this calculator prove every identity?

No. It gives strong numeric evidence and helpful hints. A formal proof still needs algebraic steps using accepted identities.

2. Why are some test points skipped?

Some angle values can create division by zero or undefined trig values. The calculator skips those domain points safely.

3. Which variable should I use?

Use x unless your expression needs another single variable. Enter the same variable name in both sides.

4. Should I use radians or degrees?

Use radians for most advanced math work. Use degrees when your classroom example or worksheet clearly uses degree measure.

5. What does tolerance mean?

Tolerance is the allowed difference between both sides. A smaller value makes the test stricter.

6. Can I enter powers?

Yes. Use the caret sign. For example, enter sin(x)^2 instead of sin2x.

7. Does a likely result guarantee a proof?

No. It means both sides matched at tested values. Always finish with a written symbolic proof.

8. What exports are available?

You can download a CSV file for spreadsheets. You can also download a PDF report for records or lessons.

Related Calculators

Paver Sand Bedding Calculator (depth-based)Paver Edge Restraint Length & Cost CalculatorPaver Sealer Quantity & Cost CalculatorExcavation Hauling Loads Calculator (truck loads)Soil Disposal Fee CalculatorSite Leveling Cost CalculatorCompaction Passes Time & Cost CalculatorPlate Compactor Rental Cost CalculatorGravel Volume Calculator (yards/tons)Gravel Weight Calculator (by material type)

Important Note: All the Calculators listed in this site are for educational purpose only and we do not guarentee the accuracy of results. Please do consult with other sources as well.