Convert sums a cos(x) + b sin(x) to R cos(x ± α) or R sin(x ± α) and apply these to sketch graphs.

u2-t4-s3-d4

Interactive

a cos x + b sin x as R cos(x − α)

manipulative

Scrub x to stack a cos x and b sin x ordinates into one sum wave; a/b sliders and an R-form overlay show amplitude R and phase.

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