Four Dials, and One of Them Lies

You'll learnto see how each of four constants reshapes the parent sine wave, one at a time.

Every sinusoid is a·sin(b(x − h)) + k wearing an outfit: four dials, each controlling one feature. The dials are not what they look like. The b is not the period, a negative a flips the wave without making its amplitude negative, and the h can hide inside an unfactored argument where it will be read wrong every time.

8 STEPS · 6 QUICK CHECKS · AMPLITUDE · MIDLINE · PERIOD · PHASE · v2

factor before you read the shift

Before you start

What you're looking at

The parent wave with a table pairing each parameter (a, b, h, k) to its one visible effect.

The question

Change one dial while the other three hold — what does it do to the wave?

Watch for

b setting the period through 2π/|b|, a negative a flipping without a negative amplitude, and factoring before reading h.

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