Amplitude Period Phase Shift Calculator Online

Calculator

Function type

Angle unit

A coefficient

B coefficient

C coefficient

D coefficient

Evaluate at x

Table start

Table end

Table step

Decimal precision

Example Data Table

This example uses y = 2 sin(3x - 45) + 1 in degrees.

Input	Value	Result
A	2	Amplitude = 2
B	3	Period = 120 degrees
C	-45	Phase shift = 15 degrees right
D	1	Midline = y = 1

Formula Used

The calculator uses the transformed trigonometric model:

y = A f(Bx + C) + D

For sine and cosine, amplitude = |A|.

For sine and cosine, period = 2π / |B| in radians, or 360° / |B| in degrees.

For tangent, period = π / |B| in radians, or 180° / |B| in degrees.

Phase shift = -C / B. A positive result shifts right. A negative result shifts left.

Vertical shift = D. The midline is y = D.

How to Use This Calculator

Select sine, cosine, or tangent.
Choose degrees or radians.
Enter A, B, C, and D from your equation.
Use the form y = A f(Bx + C) + D.
Add an x value if you want a function value.
Set table start, end, and step values.
Press Calculate to show results above the form.
Use CSV or PDF buttons to download your work.

Understanding the Calculator

Amplitude, period, phase shift, and vertical shift describe a transformed trigonometric graph. This calculator reads the model y = A f(Bx + C) + D. The symbol f can be sine, cosine, or tangent. Each coefficient changes one visible feature. The tool separates those features and shows the final equation.

Why These Values Matter

Amplitude measures height from the midline for sine and cosine. A larger value stretches the wave. A negative value reflects the graph across its midline. Period tells how long one full cycle takes. Phase shift moves the graph left or right. Vertical shift moves the midline up or down. These values make graph sketching faster. They also help with signals, sound waves, tides, rotation, and repeated motion.

Advanced Inputs

The calculator accepts radians or degrees. Use degrees for school graphing work. Use radians for calculus, physics, and engineering tasks. You can enter an evaluation point. The result shows the function value at that input. You can also create a table over a custom interval. This helps compare graph points before drawing a curve.

Interpreting the Output

For sine and cosine, amplitude is the absolute value of A. The range is centered at D. Its endpoints are D minus amplitude and D plus amplitude. For tangent, amplitude is not defined. Tangent has no maximum or minimum. Its period uses 180 degrees or pi radians. The phase shift remains negative C divided by B for all three functions.

Good Practice

Keep B nonzero. A zero B value removes the repeating pattern. Use the same angle unit for C, x, and table limits. Choose a sensible step size. Too small a step can make long tables. Compare the equation and table together. This catches typing mistakes quickly.

Exporting Results

CSV export is useful for spreadsheets and classroom records. PDF export gives a neat printable summary. Both exports include key metrics and the generated table. This makes the calculator suitable for homework, tutoring, reports, and quick graph checks.

Common Use Cases

Students use these outputs when matching equations to graphs. Teachers use them to prepare examples. Technicians use periodic models for alternating signals. The same structure also fits seasonal data, wheel motion, pendulum patterns, and repeating machine cycles accurately.

FAQs

What equation form does this calculator use?

It uses y = A f(Bx + C) + D. The function f can be sine, cosine, or tangent. Enter each coefficient directly into the matching field.

How is amplitude calculated?

For sine and cosine, amplitude equals |A|. It measures the distance from the midline to a peak. Tangent has no amplitude because it is unbounded.

How is period calculated?

For sine and cosine, period is 2π / |B| in radians. In degrees, it is 360° / |B|. Tangent uses π / |B| or 180° / |B|.

What does phase shift mean?

Phase shift is the horizontal movement of the graph. The formula is -C / B. Positive values move the graph right. Negative values move it left.

What is vertical shift?

Vertical shift is D in the model. It moves the full graph up or down. For sine and cosine, it also defines the midline y = D.

Can I use radians?

Yes. Choose radians in the unit field. Then enter C, x, and table limits in radians. The period and phase shift will also display in radians.

Why is tangent sometimes undefined?

Tangent is undefined where the cosine of its argument equals zero. The calculator marks those table values as undefined instead of forcing a false number.

What do the export buttons include?

The CSV and PDF downloads include the equation, key metrics, evaluation result, critical notes, and generated table points for your selected interval.