sin/cos/tan/φ conversion
Description
A tool for converting between phase angle φ (degrees/radians) and its sine, cosine, and tangent values, commonly used in electrical engineering and power systems.
This calculator computes the trigonometric functions of the phase shift angle φ between voltage and current in AC circuits. Input any one parameter (φ, sin φ, cos φ, or tan φ), and all others are automatically calculated.
Supported Parameters & Relationships
| Parameter | Meaning | Mathematical Relation |
|---|---|---|
| φ (°) | Phase angle in degrees | Angle between voltage and current, in degrees |
| φ (Rad) | Phase angle in radians | φ_rad = φ_deg × π / 180 |
| Sin φ | Sine of φ | sin(φ) |
| Cos φ | Cosine of φ (Power Factor) | cos(φ), i.e., Power Factor PF = P/S |
| Tan φ | Tangent of φ | tan(φ) = sin(φ)/cos(φ) |
Example Calculations
Example 1:
Given φ = 30°
Then:
- φ (Rad) ≈ 0.5236 rad
- sin φ ≈ 0.5
- cos φ ≈ 0.866 (Power Factor)
- tan φ ≈ 0.577
Example 2:
Given cos φ = 0.8
Then:
- φ ≈ 36.87°
- φ (Rad) ≈ 0.6435 rad
- sin φ ≈ 0.6
- tan φ ≈ 0.75
Example 3:
Given tan φ = 1.732
Then:
- φ ≈ 60°
- cos φ ≈ 0.5 (Power Factor)
- sin φ ≈ 0.866
Given φ = 30°
Then:
- φ (Rad) ≈ 0.5236 rad
- sin φ ≈ 0.5
- cos φ ≈ 0.866 (Power Factor)
- tan φ ≈ 0.577
Example 2:
Given cos φ = 0.8
Then:
- φ ≈ 36.87°
- φ (Rad) ≈ 0.6435 rad
- sin φ ≈ 0.6
- tan φ ≈ 0.75
Example 3:
Given tan φ = 1.732
Then:
- φ ≈ 60°
- cos φ ≈ 0.5 (Power Factor)
- sin φ ≈ 0.866
Use Cases
- Power system design and analysis
- Motor and transformer performance evaluation
- Power quality monitoring (power factor correction)
- Industrial energy efficiency optimization
- Electrical engineering exams and teaching
- Electronic circuit simulation and debugging
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