The reasoning underneath Cosine Wave
The form A cos(2π(x−h)/P)+D reaches A+D at x=h when A is positive.
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.
What the Cosine Wave model leaves out
Confusing the phase location with an angular constant changes the horizontal scale whenever the period is not 2π.
Working through Cosine Wave
Measure cycle position from h, evaluate cosine, multiply by A, and add the midline.
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.
Saving enough detail for Cosine Wave
Testing the selected branch for Cosine Wave
Trace Cosine Wave back through Amplitude coefficient A and Period. Those entries should support the displayed Cosine-wave value. For a sensitivity check, alter Phase shift only. Compare that Cosine Wave result with the first Cosine-wave value, keeping both cases visible.
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.
Preserving the Cosine Wave case
Sketch Amplitude coefficient A before running Cosine Wave. Place Period on the Cosine Wave sketch and confirm its unit.
Test a symmetric Cosine Wave case. In that Cosine Wave case, compare Period with the expected Cosine Wave scale.
Validating Cosine Wave
Estimate the order of magnitude of Cosine-wave value from Amplitude coefficient A. Apply Period exactly as the Cosine Wave problem states. A large mismatch signals a setup issue before exact Cosine Wave arithmetic is repeated.
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.