Calculator inputs
Select a calculation mode. Enter known values and calculate.
Formula used
|A|
2π ÷ |B|
π ÷ |B|
f = 1 ÷ T
ω = 2πf
(maximum − minimum) ÷ 2
How to use this calculator
- Select the calculation mode matching your available information.
- Enter equation coefficients, measurements, frequency, or wave data.
- Choose output units and decimal precision.
- Press the calculation button to view complete results.
- Review formulas, graph details, and export options.
Example data
| Input | Amplitude | Period | Phase shift | Midline |
|---|---|---|---|---|
| y = 3sin(2x) | 3 | π | 0 | y = 0 |
| y = -5cos(4x) + 1 | 5 | π/2 | 0 | y = 1 |
| y = 2sin(πx/6) - 3 | 2 | 12 | 0 | y = -3 |
| y = tan(3x) | Not applicable | π/3 | 0 | y = 0 |
| Maximum 8, minimum 2 | 3 | Unknown | Unknown | y = 5 |
Function comparison
| Function | Amplitude | Base period | Range behaviour |
|---|---|---|---|
| Sine | |A| | 2π | Bounded between D − |A| and D + |A| |
| Cosine | |A| | 2π | Bounded between D − |A| and D + |A| |
| Tangent | Not defined | π | All real outputs with vertical asymptotes |
| Cotangent | Not defined | π | All real outputs with vertical asymptotes |
| Secant | Scale factor |A| | 2π | Outside the central bounded interval |
| Cosecant | Scale factor |A| | 2π | Outside the central bounded interval |
Understanding amplitude and period
Amplitude
Amplitude measures vertical distance from a wave's midline. Negative coefficients reflect graphs but never create negative amplitude. Tangent and cotangent functions do not have amplitude.
Period
Period measures the horizontal length of one complete cycle. Larger B values produce shorter periods. Always use the absolute value of B.
Frequency and phase shift
Frequency counts cycles completed during one unit. Phase shift moves the graph horizontally. Vertical shift changes the graph's central midline.
Common mistakes
Do not confuse frequency with angular frequency. Do not ignore negative signs inside parentheses. Never divide by zero when finding period.
Frequently asked questions
What is amplitude?
Amplitude is the maximum displacement from the midline. It equals the absolute value of coefficient A.
How is period calculated?
Sine and cosine use 2π divided by |B|. Tangent and cotangent use π divided by |B|.
Can amplitude be negative?
No. Amplitude is a nonnegative distance, even when A is negative.
Does tangent have amplitude?
No. Tangent is unbounded, so amplitude is not defined.
What is phase shift?
Phase shift is the horizontal movement. It equals negative C divided by B.
What is the midline?
The midline is the central horizontal line. Its equation is y equals D.
How are period and frequency related?
They are reciprocals. Frequency equals one divided by period.
Can the calculator use degrees?
Yes. Select degrees to receive periods based on 360 or 180 degrees.
Why is B required?
B controls horizontal compression and period. A zero B removes periodic variation.