How this calculator works
Factoring B from Bx+C gives B(x-h), where h=-C/B. This h is the horizontal shift. The magnitude of A sets amplitude and D moves the midline. B controls how quickly the angle advances, giving period 2π/|B|. A negative A reflects the curve through its midline. Reversing from transformed form uses non-negative A and positive B; other coefficient choices can describe the same curve. No graph is drawn.
Formula
f(x)=A sin(Bx+C)+D or A cos(Bx+C)+D; amplitude=|A|; period=2π/|B|; phase shift=-C/B; midline y=D.
Worked example
For f(x)=2 sin(2x-π/2)+1, amplitude is 2, period is π, phase shift is π/4 to the right and f(π/4)=1.
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Frequently asked questions
Does positive C mean a right shift?
When B is positive, positive C gives a left shift because h=-C/B.
Can B be negative?
Yes. The period uses |B|, while the signed B still matters in the phase shift and point evaluation.
What if A is zero?
The result is a constant function at D. The displayed period and shift describe the chosen expression, although a constant curve has no unique fundamental period.