Calculator Inputs
Plotly Graph
The graph shows the reciprocal relation y = 1/x.
Example Data Table
Use these sample conversions to verify your understanding.
| Cotangent Input | Tangent Output | Principal Angle |
|---|---|---|
| 4 | 0.25 | 14.036° |
| 2 | 0.5 | 26.565° |
| 1 | 1 | 45° |
| 0.5 | 2 | 63.435° |
| -3 | -0.333333 | -18.435° |
| -1/2 | -2 | -63.435° |
Formula Used
Cotangent and tangent are reciprocal trigonometric functions.
Main conversion: tan(θ) = 1 / cot(θ)
Principal angle: θ = arctan(tan(θ))
Restriction: if cot(θ) = 0, tangent is undefined.
This calculator first finds the reciprocal. It then reports the principal angle in radians and degrees whenever the tangent value exists.
How to Use This Calculator
- Enter a cotangent value as a decimal or fraction.
- Choose the decimal precision you want displayed.
- Select your preferred angle display style.
- Enable the step list if you want detailed working.
- Press Convert Now to calculate the tangent.
- Review the result cards, graph, and example comparisons.
- Download the output as a CSV or PDF file.
Frequently Asked Questions
1. What does this calculator convert?
It converts a cotangent value into its tangent value. The tool also estimates the principal angle whenever the tangent result is defined.
2. What formula does it use?
The conversion uses tan(θ) = 1 / cot(θ). Since these functions are reciprocals, the tangent comes directly from dividing one by the cotangent input.
3. What happens when cotangent equals zero?
The tangent becomes undefined because division by zero is impossible. The graph still shows the reciprocal curve, but the highlighted point is omitted.
4. Can I enter fractions?
Yes. The calculator accepts simple fractions like 3/4 or -5/2, along with regular decimal values and whole numbers.
5. Why does the graph look like two branches?
The reciprocal function y = 1/x never touches zero. That creates separate positive and negative branches around the vertical asymptote at x = 0.
6. Is the displayed angle the only possible angle?
No. Tangent repeats every π radians or 180 degrees. The calculator shows the principal angle, which is the standard reference output.
7. Why would I download CSV or PDF results?
Downloads help with homework records, reports, shared notes, or study logs. CSV is convenient for spreadsheets, while PDF is useful for printing.
8. Is this calculator useful for checking manual work?
Yes. It is helpful for verifying reciprocal conversions, inspecting principal angles, and comparing results against worked trigonometry exercises.