Evaluate 2cos x and transformed cosine curves
Standard values are set for y = 2cos x. Change any option for a transformed model.
Standard 2cos x values
This example uses degrees, A = 2, B = 1, C = 0, and D = 0.
| x | cos x | 2cos x | Curve location |
|---|---|---|---|
| 0° | 1 | 2 | Maximum |
| 30° | 0.866025 | 1.732051 | Descending |
| 90° | 0 | 0 | Midline crossing |
| 180° | -1 | -2 | Minimum |
| 270° | 0 | 0 | Midline crossing |
| 360° | 1 | 2 | Cycle repeats |
Cosine calculation formula
For the standard calculator, A = 2, B = 1, C = 0, and D = 0.
Amplitude is |A|. The period is 360/|B| degrees or 2π/|B| radians.
The phase shift is −C/B. The derivative is −AB sin(Bx + C).
How to use this calculator
- Enter an x value or angle.
- Select degrees or radians.
- Keep A = 2 and B = 1 for standard 2cos x.
- Adjust phase, shift, graph limits, and samples when needed.
- Add extra angles for a multi-value table.
- Press Calculate 2cos x.
- Review the result, steps, graph, and derivative.
- Download CSV, PDF, or graph image when required.
Understanding 2cos x
The 2cos x expression is a cosine curve with amplitude two. Its central line is y equals zero. The output reaches two at its highest point. It reaches negative two at its lowest point. These limits remain true when no vertical shift exists. The default expression repeats after one full rotation. That rotation equals 360 degrees or 2π radians.
Calculate and inspect values
This calculator evaluates the expression at any chosen angle. It accepts degrees or radians. Select the unit before entering values. This prevents accidental mixed-unit answers. The result panel shows the converted cosine argument. It also lists the output and derivative. For the default expression, the derivative is negative two sine x. The derivative describes the curve's instant direction and steepness.
Graph features and transformations
Advanced controls extend the original expression without hiding its purpose. Amplitude changes the curve's height. Frequency compresses or stretches its horizontal cycle. Phase adjusts the curve's starting position. Vertical shift moves the entire curve upward or downward. The calculator then evaluates A cos(Bx plus C) plus D. Standard settings keep A at two, B at one, C at zero, and D at zero.
Choose useful graph settings
The graph makes these changes easier to see. Use graph limits to select the displayed x interval. Set a higher sample count for a smoother curve. Use fewer samples for faster testing. The highlighted marker identifies the submitted angle. The point table can evaluate several angles together. Enter numbers separated by commas, spaces, or new lines. This supports homework checks and classroom examples.
Recognize key cosine points
Cosine values follow patterns at common reference angles. At zero degrees, 2cos x equals two. At 90 degrees, it equals zero. At 180 degrees, it equals negative two. At 270 degrees, it returns to zero. At 360 degrees, the cycle returns to two. Radian values produce the same geometry. Only the angle notation changes.
Check and export your work
Check the selected unit whenever answers appear surprising. Confirm that frequency and phase use that same unit. A negative amplitude flips the curve vertically. A negative frequency reverses horizontal direction. Neither change removes the periodic pattern. Export the results as CSV for spreadsheets. Create a PDF summary for printing or sharing. Download the graph image when visual evidence is useful. It keeps routine trigonometric work organized. Reset defaults before beginning a new standard 2cos x question.
2cos x calculator FAQs
1. What does 2cos x mean?
It means two multiplied by the cosine of x. The coefficient two doubles every usual cosine output.
2. What is the range of standard 2cos x?
The range is from −2 to 2. Cosine stays between −1 and 1, then multiplication by two doubles those limits.
3. Is the default angle measured in degrees?
Yes. Degrees are selected by default. You can choose radians before calculating, graphing, or entering phase values.
4. What is the period of 2cos x?
The standard period is 360 degrees or 2π radians. Changing frequency B changes the period.
5. Why is the answer zero at 90 degrees?
Cosine of 90 degrees equals zero. Multiplying zero by two still produces zero.
6. What does a negative amplitude do?
A negative amplitude reflects the cosine curve across its midline. Its size remains the absolute value of the amplitude.
7. How do phase and phase shift differ?
Phase C is the value written inside the cosine. Phase shift is the horizontal movement, calculated as −C divided by B.
8. Can I graph transformed cosine functions?
Yes. Change A, B, C, or D to graph A cos(Bx + C) + D with the same controls.
9. Does the derivative use the selected unit?
The displayed derivative follows the entered formula convention. For strict calculus work, radians are normally preferred.
10. What is included in the CSV file?
The export includes the current settings, final result, and each table point with its argument, value, and derivative.
11. Can I export the plotted graph?
Yes. Use Download Graph PNG after a calculation. The PDF button also includes the visible result summary.