Example Data Table
| Function |
A |
B |
C |
D |
Mode |
Range |
Step |
| sin |
2 |
1 |
0 |
1 |
Radians |
-6.28 to 6.28 |
0.25 |
| cos |
1.5 |
2 |
0.5 |
-1 |
Radians |
-3.14 to 3.14 |
0.1 |
| tan |
1 |
1 |
0 |
0 |
Degrees |
-180 to 180 |
5 |
Formula Used
The calculator uses the transformed trigonometric model:
y = A · trig(B(x - C)) + D
A controls vertical stretch. B controls frequency and period. C shifts the graph left or right. D moves the graph up or down.
For sine, cosine, secant, and cosecant, period equals 2π / |B| in radians, or 360 / |B| in degrees.
For tangent and cotangent, period equals π / |B| in radians, or 180 / |B| in degrees.
How to Use This Calculator
- Select the main trigonometric function.
- Enter amplitude, frequency coefficient, phase shift, and vertical shift.
- Choose radians or degrees.
- Set the graph range and step size.
- Enable comparison when you want a second wave.
- Press the graph button to view results above the form.
- Use CSV or PDF buttons to save the output.
About the Desmos Trigonometry Graphing Calculator
A trigonometry graphing calculator helps you study waves with speed and control. It turns a symbolic rule into visible points. You can inspect how each parameter changes the shape. This tool follows a familiar graphing style, so learners can test equations before drawing them by hand. It supports sine, cosine, tangent, cosecant, secant, and cotangent. Each function can be stretched, compressed, shifted, and compared.
Why Graph Parameters Matter
Every trig graph has structure. Amplitude changes the height of sine and cosine waves. The coefficient inside the function controls period. Phase shift moves the pattern across the x axis. Vertical shift moves the midline. These ideas appear in physics, sound, engineering, tides, rotating motion, and signal analysis. Seeing them together makes the formula easier to understand.
Advanced Graph Review
The calculator creates a table from the selected x range. It also detects undefined values near asymptotes. This is important for tangent, cotangent, secant, and cosecant. Those graphs can break when division by zero occurs. The table keeps those points clear. The graph uses gaps, so the curve does not join across an asymptote.
Comparison and Export
Comparison mode is useful when checking transformations. You can place a sine wave beside a cosine wave. You can also compare two versions of the same equation. For example, change only the phase shift and watch the pattern slide. Change only B and watch the period shrink or grow. The summary cards show valid points, minimum, maximum, average, and period. These values help confirm the graph numerically.
Practical Learning Use
Students can use the table for homework checks. Teachers can prepare examples for lessons. Analysts can create quick wave samples for reports. The CSV export saves all calculated rows. The PDF export saves a compact report with formulas and sample points. Because the inputs stay visible, you can revise settings quickly and run another graph. This makes exploration simple, repeatable, and organized for many trigonometry tasks.
Frequently Asked Questions
1. What does this calculator graph?
It graphs transformed trigonometric functions using amplitude, frequency coefficient, phase shift, vertical shift, range, and step size. It supports sine, cosine, tangent, cosecant, secant, and cotangent.
2. Can I compare two trigonometric graphs?
Yes. Enable comparison mode and enter the second function values. The graph and table will include both functions for easier review.
3. What does amplitude mean?
Amplitude is the vertical multiplier. For sine and cosine, it controls wave height from the midline. Negative values reflect the graph.
4. What does B control?
B controls frequency and period. A larger absolute B usually makes the pattern repeat faster. A smaller absolute B stretches the graph horizontally.
5. Why do some values show undefined?
Tangent, cotangent, secant, and cosecant can have asymptotes. At those x values, the function divides by zero or nearly zero.
6. Should I use degrees or radians?
Use radians for most advanced mathematics. Use degrees when your problem states angles in degrees or uses values like 30, 45, 90, and 180.
7. What does the CSV export include?
The CSV export includes every generated x value and calculated y value. When comparison mode is active, it also includes the comparison y values.
8. What is the best step size?
Use a smaller step for smoother graphs. Use a larger step for faster tables. Very small steps may create too many points.