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Fundamental Trigonometric Identities Checker — result sheet
Check a supplied sine and cosine pair against the Pythagorean identity and calculate tangent and reciprocal identities when defined.
Inputs used
Results
Visual chart
Breakdown
Calculation steps
Returned data table
Formula and methodology
Formula: sin²(θ)+cos²(θ)=1; tan(θ)=sin(θ)/cos(θ); sec(θ)=1/cos(θ); csc(θ)=1/sin(θ).
The visitor supplies sine and cosine values from one angle. The page checks the Pythagorean identity within a small tolerance and then evaluates quotient and reciprocal identities, explicitly reporting undefined denominators.
This result follows the calculator's declared inputs, precision, validation boundaries, and model limits.
Input contract
- sin(θ) — minimum -1; maximum 1
- cos(θ) — minimum -1; maximum 1
Worked example
| Input | Value |
|---|---|
| sin(θ) | 0.6 |
| cos(θ) | 0.8 |
sin²θ + cos²θ = 1, tanθ = 0.75, secθ = 1.25, and cscθ = 1.6667.
Assumptions and limits
- The sine and cosine values describe the same angle.
- Each entered value lies between −1 and 1.
- Rounded inputs may produce a small identity residual.
- Tangent and secant are undefined when cosine is zero.
- Cosecant is undefined when sine is zero.
- The tool verifies values; it does not reconstruct a unique angle or choose a quadrant.
Calculator note
Source and methodology
Use the official WorldCalculate methodology policy for the source, formula, precision, and boundary standards behind this calculator.
Planning estimate, not financial, medical, legal, or professional advice. © WorldCalculate — reuse with attribution. Built and curated by Hassan ALRowaie.
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