Verify Trig Functions Calculator

Compare sine, cosine, tangent, and identity sides quickly today. Enter angles, choose units, review graphs. Clear numeric checks reveal matching trig statements with confidence.

Calculator Inputs

Undefined values are skipped in range scoring.

Custom Function Options

Use these fields when the custom comparison is selected. Phase uses the chosen angle unit.

Left side form: A × f(Bx + phase) + C
Right side form: A × f(Bx + phase) + C

Formula Used

Left side value = L
Right side value = R
Absolute difference = |L - R|
Relative gap (%) = |L - R| ÷ max(|L|, |R|, 10⁻¹²) × 100
Verified condition = Absolute difference ≤ tolerance

For custom transformed functions, each side uses this model:

y = A × f(Bx + phase) + C

How to Use This Calculator

  1. Select a preset identity or choose the custom comparison option.
  2. Enter the angle value and choose degrees, radians, or gradians.
  3. Set the tolerance. Smaller values make verification stricter.
  4. Enter a graph range and step size for range testing.
  5. Use the custom fields only for transformed function comparisons.
  6. Click the verify button to see results above the form.
  7. Download the CSV or PDF for records and reports.

Example Data Table

Example Angle Unit Identity Expected result
Basic identity 45 Degrees sin²(x) + cos²(x) = 1 Verified
Double angle 30 Degrees sin(2x) = 2sin(x)cos(x) Verified
Domain warning 90 Degrees tan(x) = sin(x) / cos(x) Undefined
Custom cofunction 40 Degrees sin(x) and cos(90 - x) Verified

Article

Why Trig Verification Matters

Trigonometric expressions often look different but represent the same value. A small calculator helps check that relationship before you submit work, build a lesson, or test a formula. It compares both sides at one angle. It also scans a full range. This gives a better view than one manual check.

What This Tool Checks

The calculator supports common identities and custom transformed functions. You can test Pythagorean, quotient, reciprocal, double angle, and negative angle rules. You can also compare two fitted trig forms. Change amplitude, multiplier, phase, and constant terms. This helps model waves, rotations, and signal style problems.

Accuracy And Tolerance

Digital trig values use floating point arithmetic. That means a true identity may still show a tiny difference. The tolerance field decides the largest allowed error. A tight value gives strict checking. A relaxed value is useful when data is rounded. The pass rate shows how often the identity stays inside that limit across the selected range.

Angles And Domains

Angles may be entered in degrees, radians, or gradians. The result also shows normalized degrees, quadrant, and reference angle. Domain warnings appear when a function is not defined. Tangent fails when cosine is zero. Secant, cosecant, and cotangent can fail at their own restricted points.

Graphs And Exports

The Plotly graph plots the left and right sides across the range. Matching lines suggest a valid identity. Gaps or spikes usually show domain trouble or a wrong expression. The CSV export stores every sampled point. The PDF export creates a readable result summary for reports, worksheets, or client records.

Best Use Cases

Use this tool for homework checks, teaching examples, construction layout math, wave comparisons, and formula review. It is not a proof engine. It gives strong numeric evidence. For formal mathematics, combine the output with algebraic steps. Always inspect undefined points. A formula can match where it exists but still fail outside its valid domain.

Practical Review Tips

Start with a wide range, then zoom near suspect angles. Use smaller steps for sharp curves. Compare the graph with the numeric table. Save exports before changing inputs. This keeps each check easy to repeat later.

FAQs

1. What does this calculator verify?

It compares two sides of a trigonometric identity or custom trig expression. It checks one selected angle and also scans a range for stronger numeric evidence.

2. Does it prove a trig identity?

No. It gives numerical verification. A formal proof still needs algebraic steps. Use the result as a checking tool before writing your final proof.

3. Why do true identities show small errors?

Computers use floating point numbers. Some decimal and trig values cannot be stored exactly. Tiny errors are normal, so the tolerance field controls acceptance.

4. What tolerance should I use?

Use 0.000001 for most school and general checks. Use a smaller tolerance for strict testing. Use a larger one when source data is rounded.

5. Why are some results undefined?

Some trig functions have restricted domains. Tangent and secant are undefined when cosine is zero. Cotangent and cosecant are undefined when sine is zero.

6. Can I use radians?

Yes. Choose radians from the unit menu. The calculator converts angles internally and reports normalized degree details for easier interpretation.

7. How does the custom comparison work?

Each side uses A × f(Bx + phase) + C. You can compare shifted, scaled, or reflected sine, cosine, tangent, secant, cosecant, and cotangent functions.

8. What do the CSV and PDF buttons export?

The CSV contains sampled angle values, both side values, differences, and status. The PDF contains a summary and a small sample table.

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