Solve cosine equations and transformed waves confidently. Review instant values, key properties, and sample points. Export results and inspect the plotted curve with ease.
This example uses y = cos(x) with degrees.
| Angle (degrees) | cos(x) |
|---|---|
| 0 | 1 |
| 30 | 0.8660254 |
| 60 | 0.5 |
| 90 | 0 |
| 120 | -0.5 |
| 180 | -1 |
Standard form: y = A cos(Bx + C) + D
Amplitude: |A|
Period: 2π / |B| for radians, or 360 / |B| for degrees
Phase shift: -C / B
Vertical shift: D
Range: [D - |A|, D + |A|]
Slope: In radians, y′ = -AB sin(Bx + C). In degrees, multiply by π / 180 because the argument is converted before evaluation.
This calculator evaluates the selected x value, builds a sample table, and plots the full curve for the chosen interval.
The cosine function describes periodic motion, wave behavior, and repeating patterns. This calculator handles a transformed cosine curve, not only the basic cos(x) expression. It helps you inspect the value at a chosen input and also understand how each constant changes the graph.
The amplitude controls vertical stretch. The frequency multiplier changes how fast the wave repeats. The phase shift moves the graph left or right. The vertical shift moves the entire curve upward or downward. Together, these values define the exact wave used in many maths problems.
A plotted curve makes repeating behavior easier to verify. Peaks, troughs, and turning points become clear when the graph is displayed over a selected interval. The sample table supports the graph by listing exact x and y values that can be checked manually or reused in classwork.
Cosine functions appear in trigonometry, sound analysis, electrical signals, seasonal models, and circular motion. They are also useful when studying derivatives, identities, and waveform shifts. This page combines direct evaluation, function properties, and exports so one calculation can support several learning tasks.
It evaluates y = A cos(Bx + C) + D, finds key properties, creates sample values, and draws the curve over your chosen interval.
Yes. Choose the unit mode before calculating. The calculator interprets the argument Bx + C using the unit you select.
Amplitude is the absolute value of A. It measures the distance from the midline to the highest or lowest point of the cosine wave.
The period is 2π divided by |B| in radian mode. In degree mode, the period is 360 divided by |B|.
The function becomes constant because the cosine argument no longer depends on x. In that case, period and phase shift are not defined.
Those inputs generate the plotted values. They control how much of the wave is shown and how many points appear in the table.
The exports include the calculated summary and the generated sample points. They are useful for reports, notes, or quick record keeping.
Yes. All numeric fields accept decimals, so you can test fractional amplitudes, noninteger frequencies, shifted angles, and custom plotting steps.
Important Note: All the Calculators listed in this site are for educational purpose only and we do not guarentee the accuracy of results. Please do consult with other sources as well.