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What are the period and amplitude of the trigonometric function $g(x) = A \sin(Bx + C) + D$ with $A, B > 0$?

Study flashcard from the deck CSAT (Suneung) essentials: original practice.

Answer

Amplitude $= A$; Period $= \frac{2\pi}{B}$; Vertical shift $= D$; Phase shift $= -\frac{C}{B}$.

Explanation

The graph oscillates between maximum $D + A$ and minimum $D - A$, completing one full oscillation over an interval of $\frac{2\pi}{B}$.

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