Trigonometry Calculator
Find the sine, cosine, tangent, cosecant, secant and cotangent of an angle given in degrees or radians. Exact values are returned at 0°, 90°, 180° and 270°
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Estimate only. Not engineering or safety advice. Check the result against the applicable standard and the equipment data, and have a competent engineer review it before it is relied on. Terms of use.
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About this calculator
This page calculates sin θ, cos θ, tan θ and 6 more results from angle and angle unit. Change any value or its unit and the result updates. The steps below show the working for the default values, so you can check each line against your own method.
Limits of this calculator
Use this for the angle of an impedance or a power factor (cos θ), for resolving a force or a phasor into components, and for a quick check on a rectangular to polar conversion. For a power factor angle from a known power factor, take the inverse cosine on a scientific calculator. To work with complex numbers use the complex number calculator; to add phasors use the phasor sum calculator.
Cross-check: 50 reference cases, calculated from textbook formulas coded separately from the engine by the same author, agree with this calculator. This is not an independent review.
Verification status: Engineering reference
Engineering reference. Formula and method documented and tested against separately coded reference calculations. Not yet Verified: the evidence listed on this page is still needed.
What this calculator checks
- The arithmetic of the published formula for the values you entered, in the units shown.
What remains unverified
- That the inputs suit your application. Take ratings, resistances and constants from the manufacturer data sheet or project specification.
Verification register entry
| Calculation author | Rahul Sharma (author) |
|---|---|
| Technical review | No independent technical review has been carried out |
| Individual professional approval | Not recorded |
| Formula reference | not recorded |
| Standard and edition | Not applicable: Pure mathematics or statistics; no electrical standard governs the method |
| Standard review state | Not applicable |
| Scope-screening note | not recorded |
| Cross-check test cases | 50 reference vectors (tests/reference_vectors.json) |
| Review date | not recorded |
| Next review date | not recorded |
| Status | Engineering reference |
Needed before this calculator can be marked Verified: reviewer name, qualification and review date; exact formula reference; formula source (textbook or standard); next review date.
Formula
Worked example
| Input | Value |
|---|---|
| Angle | 30 |
| Angle unit | Degrees (°) |
- sin θ = 0.5 cos θ = 0.866025
- tan θ = sin θ / cos θ = 0.5 / 0.866025 = 0.57735
- Check: sin² θ + cos² θ = 0.25 + 0.75 = 1
Assumptions
- The angle is measured counter-clockwise from the positive x axis, so a negative angle turns clockwise
- Choose the unit that matches your angle: 30 means 30° in degrees mode and 30 rad in radians mode
- An angle within 1e-9° of a multiple of 90° is treated as exactly that multiple, so cos 90° is 0 and not 6e-17
- Where a function is not defined (tan and sec at 90° and 270°, cot and csc at 0° and 180°) the result is a dash
- Angles beyond ±1,000,000,000° are rejected because the angle itself is no longer held with enough precision
Use this for the angle of an impedance or a power factor (cos θ), for resolving a force or a phasor into components, and for a quick check on a rectangular to polar conversion. For a power factor angle from a known power factor, take the inverse cosine on a scientific calculator. To work with complex numbers use the complex number calculator; to add phasors use the phasor sum calculator.
Inputs and results
| Input | Unit | Allowed or shown | Note |
|---|---|---|---|
| Angle | (number) | any number | Any angle, positive or negative, including more than one full turn. Choose degrees or radians below. |
| Angle unit | (choice) | Degrees (°); Radians (rad) |
| Result | Unit | Allowed or shown | Note |
|---|---|---|---|
| sin θ | (number) | Shown to 6 decimal places | |
| cos θ | (number) | Shown to 6 decimal places | |
| tan θ | (number) | Shown to 6 decimal places | |
| csc θ (1 / sin θ) | (number) | Shown to 6 decimal places | |
| sec θ (1 / cos θ) | (number) | Shown to 6 decimal places | |
| cot θ (1 / tan θ) | (number) | Shown to 6 decimal places | |
| Angle in degrees | (number) | Shown to 6 decimal places | |
| Angle in radians | (number) | Shown to 6 decimal places | |
| Equivalent angle from 0° to 360° | (number) | Shown to 6 decimal places |
How it is calculated
Each input is converted to the base unit of its quantity, the formula above is applied in the order shown in the worked example, and each result is shown in the unit you choose. Results are held at full precision and rounded only for display, except where a step selects a standard size, as the worked example shows. A value outside its allowed range is refused with a message instead of giving a result.
How the result changes with angle
| Angle | sin θ | cos θ | tan θ |
|---|---|---|---|
| 3 | 0.052336 | 0.99863 | 0.052408 |
| 7.5 | 0.130526 | 0.991445 | 0.131652 |
| 15 | 0.258819 | 0.965926 | 0.267949 |
| 30 | 0.5 | 0.866025 | 0.57735 |
| 60 | 0.866025 | 0.5 | 1.732051 |
| 120 | 0.866025 | -0.5 | -1.732051 |
| 300 | -0.866025 | 0.5 | -1.732051 |
Other inputs are the same as in the worked example above.
Standards and further reading
Complex numbers, rectangular and polar form and angle conversion are standard mathematics, not the subject of a standard. Standards apply when the result feeds an electrical design, and they set the method there.
Frequently asked questions
What do I need to enter?
Enter angle and angle unit. Change the unit of a value with its selector and the result stays the same.
What does this calculator assume?
The angle is measured counter-clockwise from the positive x axis, so a negative angle turns clockwise. Choose the unit that matches your angle: 30 means 30° in degrees mode and 30 rad in radians mode. An angle within 1e-9° of a multiple of 90° is treated as exactly that multiple, so cos 90° is 0 and not 6e-17. Where a function is not defined (tan and sec at 90° and 270°, cot and csc at 0° and 180°) the result is a dash. Angles beyond ±1,000,000,000° are rejected because the angle itself is no longer held with enough precision.
Which calculators should I use next?
Common next steps are Complex Numbers (Rectangular and Polar), Phasor Sum and Difference (Polar Inputs), Series RLC Impedance and Power Factor Correction. The related links at the bottom of this page open them.
How accurate are the results?
Every figure comes from the same tested engine as the Elecmetric calculators and is meant for estimating. 50 reference cases, calculated from textbook formulas coded separately from the engine by the same author, agree with this calculator. This is not an independent review. Check design values against the standard and the equipment data you work to.
Formula guides and reference
Longer explanations with worked examples and tables, written for the same topic.
- Trigonometry Formulas for Electrical Engineers: Sine, cosine and tangent formulas for engineers: the six trig functions, degrees and radians
- Power Factor and the Power Triangle: Power factor formulas: kW, kVA and kVAR from the power triangle, capacitor kVAR to raise power factor
- Complex Number Formulas: Polar and Rectangular: Complex number formulas for engineers: rectangular and polar form, conversion with atan2, addition
More Engineering Mathematics calculatorsAll engineering calculatorsTrigonometry (Sin, Cos, Tan) in Elecmetric