Trigonometric identities · manipulative

One wave from two terms

Drag the scrub line. At each x the height of the sum is a cos x stacked with b sin x — so the pair is always a single wave of amplitude R.

a cos x b sin x sum R form

Drag the scrub line · scroll zoom · drag background to pan

3
4

Target form

R-form overlay
thin confirmation that it matches the sum

Amplitude R

Phase angle

Working