The midline in a trigonometric graph is best described as which of the following?

The midline in a trigonometric graph is best described as which of the following?

• A. Vertical shift (up or down)
• B. Horizontal shift (left or right)
• C. Amplitude
• D. Period

Answer: (A)

The midline is the horizontal line around which a sine or cosine wave oscillates; it represents the average value of the function over a full cycle. In the standard form y = A sin(Bx - C) + D (or with cosine), the midline is y = D, which is a vertical shift up or down by D. This moves the entire graph up or down without changing its height relative to the midline. The amplitude is the distance from the midline to a peak, not the midline itself, and the period depends on B, reflecting horizontal stretching or compression. For example, y = 3 sin(2x) + 1 has a midline at y = 1, oscillates between -2 and 4, with amplitude 3 and period π.

The midline is the horizontal line around which a sine or cosine wave oscillates; it represents the average value of the function over a full cycle. In the standard form y = A sin(Bx - C) + D (or with cosine), the midline is y = D, which is a vertical shift up or down by D. This moves the entire graph up or down without changing its height relative to the midline. The amplitude is the distance from the midline to a peak, not the midline itself, and the period depends on B, reflecting horizontal stretching or compression. For example, y = 3 sin(2x) + 1 has a midline at y = 1, oscillates between -2 and 4, with amplitude 3 and period π.