Enter Sine Graph Values
Sine Graph
The chart updates from the calculated sample points.
Generated Data Table
This table shows the first twelve generated points.
| # | x | Angle Argument | y |
|---|---|---|---|
| 1 | -6.283185 | -6.283185 | 0 |
| 2 | -6.230825 | -6.230825 | 0.052336 |
| 3 | -6.178466 | -6.178466 | 0.104528 |
| 4 | -6.126106 | -6.126106 | 0.156434 |
| 5 | -6.073746 | -6.073746 | 0.207912 |
| 6 | -6.021386 | -6.021386 | 0.258819 |
| 7 | -5.969026 | -5.969026 | 0.309017 |
| 8 | -5.916666 | -5.916666 | 0.358368 |
| 9 | -5.864306 | -5.864306 | 0.406737 |
| 10 | -5.811946 | -5.811946 | 0.45399 |
| 11 | -5.759587 | -5.759587 | 0.5 |
| 12 | -5.707227 | -5.707227 | 0.544639 |
Example Data Table
Example equation: y = 2 sin(0.5(x - 30)) + 1, using degrees.
| x | Angle Argument | Approximate y | Meaning |
|---|---|---|---|
| 30 | 0° | 1 | Starts on the midline. |
| 210 | 90° | 3 | Reaches maximum value. |
| 390 | 180° | 1 | Returns to the midline. |
| 570 | 270° | -1 | Reaches minimum value. |
| 750 | 360° | 1 | Completes one full cycle. |
Formula Used
The calculator uses this transformed sine model:
y = A sin(B(x - C)) + D
- A: amplitude factor. The graph height is
|A|. - B: horizontal multiplier. Period is
2π / |B|in radians. - B: in degree mode, period is
360 / |B|. - C: phase shift. Positive values move the graph right.
- D: vertical shift and midline value.
- Range:
[D - |A|, D + |A|]. - Area: estimated by the trapezoidal rule over the selected range.
How to Use This Calculator
- Enter amplitude A to set the graph height.
- Enter multiplier B to control the period.
- Enter phase shift C to move the curve horizontally.
- Enter vertical shift D to move the midline.
- Choose radians or degrees.
- Set the x-range for the graph.
- Increase sample points for a smoother chart.
- Press the calculate button to show results above the form.
- Use CSV or PDF buttons to save the output.
Understanding Sine Function Graphs
Why Sine Graphs Matter
A sine graph shows smooth repeating motion. It is used in trigonometry, waves, sound, tides, voltage, and circular motion. This calculator helps you study that shape with controlled inputs and clear outputs.
Main Equation
The model is y = A sin(B(x - C)) + D. The value A controls height. Its absolute value is the amplitude. The value B controls compression or stretching along the x-axis. The value C moves the curve left or right. The value D moves the midline upward or downward.
Shape and Movement
A normal sine wave starts at zero, rises to one, returns to zero, falls to minus one, and repeats. When you change amplitude, the highest and lowest values change. When you change period, the wave repeats sooner or later. When you change phase, the same wave begins at a different x location.
Advanced Graph Features
The calculator also estimates useful graph features. It reports period, midline, output range, roots, local maximum points, local minimum points, signed area, absolute area, and average value. These values help you compare equations without drawing every point manually.
Radians and Degrees
Use radians when working with calculus, physics, and most advanced math. Use degrees when your class or worksheet measures angles from zero to three hundred sixty. Both modes use the same sine idea. Only the angle conversion changes.
Exports and Tables
The graph gives a quick visual check. A data table gives exact sample points. CSV export helps you move results into spreadsheets. PDF export creates a simple report for notes, homework, or teaching.
Accuracy Tips
For best results, choose a wide x-range. Include at least one full period when possible. Increase sample count for smoother curves. Use fewer samples for quick checks. Always review the formula and input units before using the final answer.
Common Mistakes
Students often make mistakes by confusing amplitude with period. Amplitude is vertical. Period is horizontal. Another common mistake is using degrees in a radians problem. This tool keeps the unit choice visible. It also shows the internal angle argument, so you can trace each value. Teachers can use the example table to explain cycles. Learners can change one number at a time and see how the curve responds. This makes pattern recognition faster and graph interpretation more reliable overall.
FAQs
1. What does amplitude mean in a sine graph?
Amplitude is the distance from the midline to a maximum or minimum point. In the formula, it equals the absolute value of A. A larger amplitude makes the graph taller. A negative A reflects the graph across its midline.
2. How is the period calculated?
For radians, the period is 2π divided by the absolute value of B. For degrees, the period is 360 divided by the absolute value of B. The period tells how far the graph travels before repeating.
3. What is phase shift?
Phase shift moves the sine wave left or right. In this calculator, C is used inside x minus C. A positive C shifts the curve right. A negative C shifts it left.
4. What does vertical shift do?
Vertical shift moves the entire graph upward or downward. It also sets the midline. If D is 3, the sine wave oscillates around y = 3 instead of y = 0.
5. Should I use radians or degrees?
Use radians for calculus, physics, and most advanced math. Use degrees when your problem gives angles in degrees. The selected unit must match your x-values and phase shift.
6. Why are roots sometimes missing?
Roots are x-values where y equals zero. A shifted sine graph may not cross the x-axis. If zero is outside the output range, no root exists in any interval.
7. What sample count should I choose?
Use more sample points for a smoother curve and better area estimates. A value from 200 to 500 works well for most graphs. Very high values can make the page slower.
8. Can I export my sine graph data?
Yes. Use the CSV button to export x-values and y-values. Use the PDF button to save a short report with equation details, summary values, and sample rows.