In a sine or cosine function, what does amplitude measure?

In a sine or cosine function, what does amplitude measure?

• A. The vertical distance from the midline to a crest or trough
• B. The horizontal distance between consecutive peaks
• C. The vertical shift of the midline
• D. The horizontal shift of the graph

Answer: (A)

Amplitude describes how tall the wave is. The sine and cosine graphs oscillate around a midline, which is a horizontal line the graph centers on. The amplitude is the vertical distance from that midline to a crest (top) or to a trough (bottom). It’s also half the distance between a crest and a trough. In a function written as y = A sin(Bx) + D, the amplitude is |A|, so changing A makes the graph taller or shorter without moving the midline or changing where it starts. The vertical shift D moves the midline up or down, the horizontal shift (phase shift) moves the graph left or right, and the distance between consecutive peaks (the period) is 2π/|B|, not amplitude.

Amplitude describes how tall the wave is. The sine and cosine graphs oscillate around a midline, which is a horizontal line the graph centers on. The amplitude is the vertical distance from that midline to a crest (top) or to a trough (bottom). It’s also half the distance between a crest and a trough. In a function written as y = A sin(Bx) + D, the amplitude is |A|, so changing A makes the graph taller or shorter without moving the midline or changing where it starts. The vertical shift D moves the midline up or down, the horizontal shift (phase shift) moves the graph left or right, and the distance between consecutive peaks (the period) is 2π/|B|, not amplitude.