Trigonometric Functions
Graphing Sine, Cosine and Tangent Functions
Explore how trigonometric functions behave by adjusting their parameters. Observe the changes in amplitude, period, and phase shift on the graph!
Sine Function
Current Function:
f(x) = sin(x)
Observation:
The sine function produces a smooth, periodic wave that oscillates between -1 and 1 with a period of 2π.
The Mathematics Behind Trigonometric Functions
Key Concepts:
Trigonometric functions relate angles to ratios of sides in right triangles and produce periodic waves:
- Amplitude: The height of the wave from center to peak
- Period: The length of one complete cycle of the wave
- Frequency: How many cycles occur in 2π radians
- Phase Shift: Horizontal displacement of the wave
Real-world Applications:
Trigonometric functions model periodic phenomena like sound waves, light waves, alternating current, tides, and seasonal patterns. They're essential in physics, engineering, music, and many other fields.
