Midline in a sine or cosine graph is best described as:

Midline in a sine or cosine graph is best described as:

• A. The vertical axis of symmetry
• B. The horizontal axis itself
• C. The line at y = 1
• D. The horizontal line around which the graph oscillates

Answer: (D)

The midline is the horizontal line around which a sine or cosine wave oscillates. In the standard form y = A sin(Bx − C) + D (or y = A cos(Bx − C) + D), this midline is y = D—the vertical shift of the graph. It sits halfway between the maximum and minimum values, so the amplitude (the distance from the midline to a peak or to a trough) is the same above and below this line. This midline is not the vertical axis of symmetry, and the horizontal axis itself is only the midline when there’s no vertical shift (D = 0). It’s also not necessarily the line y = 1 unless the graph’s vertical shift happens to be 1. For example, a wave y = 3 sin(2x) − 2 has a midline at y = −2 and an amplitude of 3, so the peaks reach y = 1 and the troughs reach y = −5.

The midline is the horizontal line around which a sine or cosine wave oscillates. In the standard form y = A sin(Bx − C) + D (or y = A cos(Bx − C) + D), this midline is y = D—the vertical shift of the graph. It sits halfway between the maximum and minimum values, so the amplitude (the distance from the midline to a peak or to a trough) is the same above and below this line. This midline is not the vertical axis of symmetry, and the horizontal axis itself is only the midline when there’s no vertical shift (D = 0). It’s also not necessarily the line y = 1 unless the graph’s vertical shift happens to be 1. For example, a wave y = 3 sin(2x) − 2 has a midline at y = −2 and an amplitude of 3, so the peaks reach y = 1 and the troughs reach y = −5.