sine graph with max at 0,5 and min at pi/2, 1, what would the graph look like, and what would the equation be?

Answer 1

The peak-to-peak amplitude would be 5 - 1 = 4.

From its midline, the graph would go up 2, and then down 2. So the midline is located at 1 + 2, or 3. Thus we need a vertical shift (displacement) of 3 to move the standard midline of 0 up to 3.

Half of 4, or 2, is the vertical stretch.

The minimum occurs after the maximum, so there is no x-axis reflection.

The distance from the maximum to the minimum along the axis is π/2, so the full cycle is twice this amount, or π. The normal period of a sine wave is 2π, so this is happening at twice the normal rate. So, the horizontal shrink is 1/2.

Since the maximum y-value occurs at 0, this requires a left shift of π/2.

Putting all these facts together, we determine that:

y = 2sin(2x+π/2) + 3

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