High School Trigonometric Function Grapher
Visualize y = A sin(B(x – C)) + D with real-time transformations.
About the Trigonometric Function Grapher
Trigonometric functions like sine and cosine are periodic, meaning they repeat their values in regular intervals. These functions model wave-like phenomena such as sound, light, and tides. The general form of a sinusoidal function is:
Each variable transforms the parent graph in a specific way:
- Amplitude (A): Determines the vertical stretch. It represents the distance from the midline to the peak (maximum) or trough (minimum). The graph oscillates between D – |A| and D + |A|.
- Frequency Parameter (B): Affects the horizontal stretch or compression. It determines the Period of the function, which is the length of one full cycle. Formula: Period = 2Ï€ / |B|.
- Phase Shift (C): Shifts the graph horizontally. If the formula is written as B(x – C), then C is the shift to the right. Note: Sometimes this is written as Bx – C’, in which case the shift is C’/B. This tool uses the factored form B(x – C) for clarity.
- Vertical Shift (D): Shifts the graph up or down. This value becomes the new “Midline” of the wave.
Using the Trigonometric Function Grapher
This tool allows you to manipulate these four parameters independently. By adjusting the sliders or inputs, you can instantly see how changing the Amplitude makes the wave taller, or how altering the Phase Shift slides the wave left or right. The graph axes are scaled in units of Pi (Ï€), which is standard for trigonometric analysis.
FAQ
Yes, this tool is completely free and open-source for educational use.
In calculus and higher mathematics, radians are the natural unit for angles because they relate the arc length directly to the radius. This grapher uses radians (multiples of π) on the x-axis.
Currently, this tool focuses on Sine and Cosine to clearly demonstrate wave properties like amplitude and phase shift, which are less intuitive for Tangent functions due to asymptotes.
For sine and cosine, Period = 2Ï€ / B.