Trigonometry Function Plotter
Use this calculator to generate a table of (x, y) coordinates for common trigonometric functions (Sine, Cosine, Tangent) based on your specified amplitude, frequency, phase shift, and vertical shift. You can define the range of x-values and the number of points to calculate, providing data that can be used to plot the function's graph.
Calculated Points:
| X (radians) | Y Value |
|---|---|
| " + x.toFixed(4) + " | " + y.toFixed(4) + " |
Understanding Trigonometric Functions and Their Graphs
Trigonometric functions are fundamental in mathematics, physics, engineering, and many other fields. They describe relationships between angles and sides of triangles, and when plotted on a coordinate plane, they produce characteristic wave-like patterns. The most common trigonometric functions are Sine (sin), Cosine (cos), and Tangent (tan).
The General Form of a Sinusoidal Function
The general form for sine and cosine functions is often expressed as: y = A sin(B(x - C)) + D or y = A cos(B(x - C)) + D. Each parameter plays a crucial role in shaping the graph:
- Amplitude (A): This value determines the maximum displacement or distance from the function's midline. A larger amplitude means a taller wave. For example, if A=2, the wave will reach twice as high and low compared to A=1.
- Frequency Factor (B): This parameter affects the period of the function, which is the length of one complete cycle of the wave. The period is calculated as
2π / Bfor sine and cosine. A larger 'B' value means the wave completes more cycles in a given interval, making it appear "compressed" horizontally. - Phase Shift (C): Also known as horizontal shift, 'C' determines how much the graph is shifted horizontally from its usual position. A positive 'C' shifts the graph to the right, while a negative 'C' shifts it to the left. The shift is by 'C' units.
- Vertical Shift (D): This value determines the vertical position of the function's midline. A positive 'D' shifts the entire graph upwards, and a negative 'D' shifts it downwards. The midline is the horizontal line
y = D.
The Tangent Function
The tangent function, y = A tan(B(x - C)) + D, behaves differently from sine and cosine. While sine and cosine produce continuous waves, the tangent function has vertical asymptotes where the function is undefined (typically where cos(B(x-C)) = 0). Its graph consists of repeating branches that extend infinitely upwards and downwards, with a period of π / B.
How to Use the Trigonometry Function Plotter
- Select Function: Choose whether you want to plot a Sine, Cosine, or Tangent function from the dropdown menu.
- Set Parameters (A, B, C, D): Input the desired values for Amplitude, Frequency Factor, Phase Shift (in radians), and Vertical Shift.
- Define X-Range: Enter the 'Start X Value' and 'End X Value' to specify the interval over which you want to generate points. These values should be in radians.
- Specify Number of Points: Choose how many (x, y) coordinate pairs you want the calculator to generate within your defined range. More points will give a more detailed representation of the curve.
- Generate Points: Click the "Generate Points" button. The calculator will then display a table of x and corresponding y values, which you can use to manually plot the graph or understand the function's behavior.
Example: Plotting a Modified Sine Wave
Let's say you want to plot the function y = 2 sin(0.5(x - 1)) + 3 from x=0 to x=10 with 100 points.
- Function Type: Sine
- Amplitude (A): 2
- Frequency Factor (B): 0.5
- Phase Shift (C): 1
- Vertical Shift (D): 3
- Start X Value: 0
- End X Value: 10
- Number of Points: 100
After entering these values and clicking "Generate Points," the calculator will produce a table of 100 (x, y) pairs for this specific sine wave, showing its amplitude of 2, a period of 2π / 0.5 = 4π, shifted 1 unit to the right, and with a midline at y=3.