Enter Cosine Wave Inputs
Example Data Table
| x Input | x in Radians | Cosine Output |
|---|---|---|
| 0 | 0 | 6 |
| 30 | 0.523599 | 3.500000 |
| 60 | 1.047198 | -1.500000 |
| 90 | 1.570796 | -4.000000 |
| 120 | 2.094395 | -1.500000 |
Use the inputs above to replace the sample rows with your generated cosine values. The table supports study checks, plotting, and export workflows.
Formula Used
General cosine wave: y = A cos(ωx + φ) + D
A is amplitude, which controls peak height from the midline.
ω is angular frequency, where ω = 2πf.
φ is phase shift, moving the wave left or right.
D is vertical shift, moving the entire graph upward or downward.
Period: T = 1 / f. Maximum = D + |A|. Minimum = D - |A|. Peak-to-peak = 2|A|.
This calculator evaluates the selected x input and also builds a full value table across your chosen range and interval.
How to Use This Calculator
- Enter the amplitude to define the wave height from the midline.
- Enter the frequency to set how quickly the cosine cycle repeats.
- Provide the phase shift and choose degrees or radians.
- Enter the vertical shift and the x value for direct evaluation.
- Choose the table start, end, and step values for generated points.
- Click the calculate button to show results above the form.
- Use the CSV or PDF buttons to save the generated table.
Why This Cosine Wave Calculator Helps
This tool supports trigonometry practice, physics wave problems, signal studies, and graph preparation. It calculates a direct cosine value, shows core wave properties, and generates a reusable point table for plotting or reporting.
Because the input layout adapts from three columns on large screens to two and one on smaller devices, the calculator remains easy to use across desktops, tablets, and phones.
FAQs
1. What does amplitude mean in a cosine wave?
Amplitude is the distance from the midline to a peak or trough. Larger amplitude creates taller waves, while smaller amplitude produces flatter waves.
2. What is the period of a cosine function?
The period is one complete cycle length. In this calculator, period equals 1 divided by frequency, showing how often the wave repeats.
3. Why is phase shift important?
Phase shift moves the cosine graph horizontally. It is useful when matching observed data, aligning signal timing, or solving transformed trigonometric equations.
4. Can I use degrees instead of radians?
Yes. Choose degrees when your angle inputs are in standard classroom form. Choose radians when working with calculus, physics, or more advanced modeling.
5. What does vertical shift change?
Vertical shift moves the whole cosine wave upward or downward. It also changes the midline, maximum value, and minimum value.
6. Why generate a value table?
A table gives evenly spaced x values and outputs, making graph plotting easier. It also helps verify homework, lab data, or simulation assumptions.
7. Does this calculator support exports?
Yes. Use CSV export for spreadsheet work and PDF export for printable notes, reports, or saved reference documents.
8. Where can this calculator be used?
It is useful in mathematics, acoustics, electronics, signal processing, and mechanics wherever periodic cosine behavior must be evaluated or documented.