Trigonometric Graphs Visualizer
Explore sin, cos, and tan graphs with adjustable amplitude, frequency, and phase shift. See how transformations affect the wave in real-time.
Function
Equation
| Formula | y = sin(x) |
| Period | 2π |
| Amplitude | 1.0 |
| Max | 1.0 |
| Min | -1.0 |
Understanding Trig Transformations
General Form
- Standard form: y = A·sin(B(x - C)) + D
- A = Amplitude (vertical stretch/compression)
- B = Frequency (horizontal stretch/compression)
- C = Phase shift (horizontal translation)
- D = Vertical shift (vertical translation)
Key Properties
- Period = 2π/B
- Maximum = A + D
- Minimum = -A + D
- Midline: y = D
Function Characteristics
| Function | Period | Range | Zeros |
|---|---|---|---|
| sin(x) | 2π | [-1, 1] | nπ |
| cos(x) | 2π | [-1, 1] | π/2 + nπ |
| tan(x) | π | (-∞, ∞) | nπ |
Applications
- Sound waves and acoustics
- Electromagnetic waves
- Oscillations and vibrations
- Circular motion
- Seasonal patterns
You're crushing it!