Calculated Results
Transformation analysis
Curve comparison
Key points
| Function | Point type | x exact | x decimal | y |
|---|
Generated value table
Formula Used
Cosine form: y = A cos(Bx + C) + D
Amplitude: |A|
Period: 2π / |B| in radians
Phase shift: −C / B
Midline: y = D
Range: [D − |A|, D + |A|]
Amplitude controls vertical height. Frequency controls each cycle’s width. Phase and vertical shifts move the entire curve.
How to Use This Calculator
Choose radians or degrees. Enter each function’s four transformation values. Select graph, table, comparison, and export preferences carefully.
Press calculate and graph. Review properties, intersections, and highlighted key points. Adjust settings until the visualization matches your needs.
Use presets for practice. Export the graph, table, or printable report. Share links preserve the calculator’s current input settings.
Example Data Table
| Function | A | B | C | D | Amplitude | Period |
|---|---|---|---|---|---|---|
| y = 2 sin(x) | 2 | 1 | 0 | 0 | 2 | 2π |
| y = cos(2x) | 1 | 2 | 0 | 0 | 1 | π |
| y = −sin(x) + 1 | −1 | 1 | 0 | 1 | 1 | 2π |
| y = 3 cos(x − π/2) | 3 | 1 | −π/2 | 0 | 3 | 2π |
Frequently Asked Questions
What does amplitude represent?
Amplitude measures distance from the midline. It equals the absolute value of A. Larger amplitudes create taller waves around the selected midline.
How is the period calculated?
The period measures one complete cycle. In radians, divide 2π by absolute B. In degrees, divide 360 by absolute B instead.
What is the phase shift?
Phase shift moves the graph horizontally. Calculate it using negative C divided by B. Positive results shift right, while negatives shift left.
Why can sine and cosine overlap?
Sine and cosine share identical wave shapes. Their standard graphs differ by one quarter-period. Suitable phase shifts can make both curves coincide exactly.
Can I graph several functions?
Yes, enable both primary curves. Two additional custom expressions are also available. Derivative and integral overlays can provide further comparisons.
How are intersections estimated?
The calculator samples differences between enabled primary curves. Sign changes identify likely crossings for numerical refinement. Very close tangent intersections may require higher sampling resolution.
What custom expressions are supported?
Expressions may include x and common mathematical functions. Parentheses, powers, constants, and arithmetic operators are supported. Invalid or unsafe expressions are rejected before graphing.
Can results use degrees?
Yes, select degrees before calculating. Primary functions then interpret x and phase values accordingly. The graph can still display decimal or degree labels.
How can I export my work?
Use the export buttons below. Download tables, images, SVG graphics, or PDF reports. Printing and shareable input links are also available.