Why this relationship works
The form A cos(2π(x−h)/P)+D reaches A+D at x=h when A is positive.
For this page, cosine wave is interpreted under the stated convention and input order.
Math calculator
Cosine Wave Calculator
Evaluate a cosine wave using explicit period and horizontal phase shift. The calculation trail makes the reported cosine-wave value easier to reproduce.
Cosine Wave inputs
Values for this result
Where Cosine Wave applies
Cosine form is convenient when a periodic record begins at a peak or trough.
Where the shortcut stops
Confusing the phase location with an angular constant changes the horizontal scale whenever the period is not 2π.
Compare the result with the worked example's scale before relying on the reported cosine-wave value.
A worked example
At x equal to phase shift 1, a wave with A=2 and D=−1 returns 1. This Cosine Wave example can be compared with sine form.
Working through Cosine Wave
Measure cycle position from h, evaluate cosine, multiply by A, and add the midline.
From calculation to usable answer
Source values may arrive in a different order from the form. Map them explicitly to amplitude coefficient a, period, phase shift, vertical shift d and evaluation x, normalize units, and retain enough precision for the next step after cosine-wave value.
How the output responds
A half-period move reverses the displacement from the midline. Watching this response separates a data-entry mistake from an unexpected but valid value.
Precision and reporting
If amplitude coefficient a, period, phase shift, vertical shift d and evaluation x are exact counts, more result digits may be meaningful than when they are measured approximations. Let the least certain source guide the final presentation.
Sine form describes the same family with a quarter-period phase adjustment. This page deliberately reports only the former interpretation.
Label the output as cosine-wave value in notes or tables. Store amplitude coefficient a, period, phase shift, vertical shift d and evaluation x beside it when the result will be reused in a later stage.
Testing the selected branch for Cosine Wave
Cosine Wave uses Amplitude coefficient A, Period, Phase shift, Vertical shift D, and Evaluation x. Check the value at the phase shift, where an unreflected cosine begins at its peak, then repeat the test one full period later.
For this cosine wave result, keep period, phase shift, horizontal units, and midline together; separating those parameters can describe a different wave with a similar-looking value.
Questions about Cosine Wave
What does Cosine Wave calculate?
The form A cos(2π(x−h)/P)+D reaches A+D at x=h when A is positive.
When is Cosine Wave useful?
Cosine form is convenient when a periodic record begins at a peak or trough.
What can make Cosine Wave misleading?
Confusing the phase location with an angular constant changes the horizontal scale whenever the period is not 2π.