Vertical Shift Calculator
Find vertical shift and midline of a sine or cosine graph
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Vertical Shift Formula
midline: y = D
Vertical shift moves a sine or cosine graph up or down. In standard form, the constant D gives both the vertical shift and the graph midline.
⚠ This calculator reads D from y=A sin(Bx+C)+D or y=A cos(Bx+C)+D. Positive D shifts upward, negative D shifts downward.
How Vertical Shift Works
The sinusoidal wave oscillates around its midline. Adding D changes that center line without changing amplitude or period.
Constant D
The added constant controls shift.
Midline
The midline is y=D.
Up or Down
Positive shifts up, negative shifts down.
Separate From Amplitude
Amplitude controls wave height.
💡 Example: For y=3cos(x)-2, D=-2 and the midline is y=-2.
Applications of Vertical Shift
Trig Graphs Sinusoidal Models Tides Wave Data
Frequently Asked Questions
What is a vertical shift calculator?▼
It identifies the vertical shift and midline of a sine or cosine function.
What is the vertical shift formula?▼
For y=A sin(Bx+C)+D or y=A cos(Bx+C)+D, the vertical shift is D and the midline is y=D.
How do I use this calculator?▼
Enter the constant D and click Calculate.
Is vertical shift the same as amplitude?▼
No. Amplitude controls height from the midline, while vertical shift moves the midline up or down.
Where is vertical shift used?▼
It is used in trig graphing, sinusoidal modeling, waves, tides, and data fitting.
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